Functional-differential equations in Sobolev spaces and related problems of spectral theory

V. V. Vlasov ; D. A. Medvedev

Contemporary Mathematics. Fundamental Directions, Functional differential equations, Tome 30 (2008), pp. 3-173.

Bibliographie

[1] Avdonin S. A., Ivanov S. A., “Bazisy Rissa iz eksponent i razdelennykh raznostei”, Algebra i Analiz, 13:3 (2001), 1–17 | MR

[2] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991 | MR | Zbl

[3] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Elementy sovremennoi teorii funktsionalno-differentsialnykh uravnenii (metody i prilozheniya), In-t kompyut. issled., M., 2002

[4] Aliev R. G., “O razreshimosti uravnenii s otklonyayuschimsya argumentom v gilbertovom prostranstve”, Dokl. AN SSSR, 247:6 (1979), 1289–1291 | MR

[5] Aliev R. G., “Ob asimptoticheskom povedenii reshenii uravnenii s otklonyayuschimsya argumentom v gilbertovom prostranstve”, Differ. uravn., 17:3 (1981), 558–561 | MR | Zbl

[6] Aliev R. G., “Ob ustoichivosti reshenii uravnenii s zapazdyvayuschim argumentom v gilbertovom prostranstve”, Differ. uravn., 23:4 (1987), 555–568 | MR | Zbl

[7] Antonevich A. B., Lineinye funktsionalnye uravneniya. Operatornyi podkhod, Izd-vo “Universitetskoe”, Minsk, 1988 | MR | Zbl

[8] Akhmerov R. R., Kamenskii M. I., Potapov A. S. i dr., “Teoriya uravnenii neitralnogo tipa”, Itogi nauki i tekhniki. Ser. Mat. analiz, 19, VINITI, M., 1981, 55–126 | MR | Zbl

[9] Bagirov L. A., Kondratev V. A., “Ob asimptotike reshenii differentsialnykh uravnenii v gilbertovom prostranstve”, Mat. sb., 182:4 (1991), 508–525 | MR | Zbl

[10] Birkgan S. E., Eksponentsialnaya dikhotomiya i ustoichivost reshenii differentsialno-raznostnykh uravnenii neitralnogo tipa s pochti periodicheskimi koeffitsientami, Diss. $\dots$ kand. fiz.-matem. nauk, Voronezh, 1985

[11] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, Mir, M., 1967 | MR | Zbl

[12] Berezanskii L. M., “Polozhitelnost funktsii i ustoichivost lineinykh differentsialnykh uravnenii s posledeistviem”, Differ. uravn., 26:9 (1990), 1490–1500 | MR | Zbl

[13] Borok V. M., Zhitomirskii Ya. I., “O zadache Koshi dlya uravnenii v chastnykh proizvodnykh s otklonyayuschimsya argumentom”, Differentsialnye uravneniya s otklonyayuschimsya argumentom, Naukova dumka, Kiev, 1977, 1289–1293

[14] Bradulina E. V., “O razreshimosti differentsialno-raznostnykh uravnenii neitralnogo tipa v prostranstvakh Soboleva”, Nekotorye problemy fundamentalnoi i prikladnoi matematiki i ikh prilozheniya v zadachakh fiziki, MFTI, M., 2005, 24–39

[15] Vasyunin V. I., “Bezuslovno skhodyaschiesya spektralnye razlozheniya i zadacha interpolyatsii”, Trudy Mat. in-ta im. V. A. Steklova, 130, Nauka, M., 1978, 5–49 | MR

[16] Vlasenko L. A., Evolyutsionnye modeli s neyavnymi i vyrozhdennymi differentsialnymi uravneniyami, Sistemnye tekhnologii, Dnepropetrovsk, 2006

[17] Vlasenko L. A., Rutkas A. G., “Teoremy edinstvennosti i approksimatsii dlya odnogo vyrozhdennogo operatorno-differentsialnogo uravneniya”, Mat. zametki, 60:4 (1996), 597–601 | MR | Zbl

[18] Vlasenko L. A., Rutkas A. G., “Ob odnoznachnoi razreshimosti odnogo vyrozhdennogo fuktsionalno-differentsialnogo uravneniya”, Dopovidi NAN Ukraïni, 3 (2003), 11–16 | MR

[19] Vlasov V. V., “Kratnaya minimalnost chasti sistemy kornevykh vektorov puchka M. V. Keldysha”, Dokl. AN SSSR, 263:6 (1982), 1289–1293 | MR | Zbl

[20] Vlasov V. V., “O $k$-kratnoi minimalnosti kornevykh vektorov puchkov keldyshevskogo tipa”, Mat. fizika. AN SSSR, 1982, no. 32, 80–89 | MR | Zbl

[21] Vlasov V. V., “O kraevykh zadachakh dlya odnogo klassa integrodifferentsialnykh uravnenii i svyazannykh s nimi spektralnykh voprosakh”, Dokl. AN SSSR, 303:6 (1988), 1293–1296 | Zbl

[22] Vlasov V. V., “O razreshimosti kraevykh zadach dlya odnogo klassa integrodifferentsialnykh uravnenii na poluosi”, Differnts. uravneniya, 25:9 (1989), 1589–1599 | MR | Zbl

[23] Vlasov V. V., “O kratnoi minimalnosti chasti sistemy kornevykh vektorov nekotorykh operator-funktsii”, Dokl. AN SSSR, 310:2 (1990), 276–280 | MR | Zbl

[24] Vlasov V. V., “Ob ustoichivosti reshenii odnogo klassa integrodifferentsialnykh uravnenii na poluosi”, Nekotorye problemy matematiki v zadachakh fiziki, mekhaniki, ekonomiki, Mezhduvedomstvennyi sbornik nauchnykh trudov, MFTI, M., 1990, 33–45

[25] Vlasov V. V., “O razreshimosti odnogo klassa funktsionalno-differentsialnykh uravnenii na poluosi i nekotorykh spektralnykh voprosakh”, Dokl. AN SSSR, 319:1 (1991), 22–26 | Zbl

[26] Vlasov V. V., “O povedenii reshenii nekotorykh klassov differentsialno-raznostnykh uravnenii s operatornymi koeffitsientami”, Izv. vuzov. Mat., 1992, no. 8(363), 80–83 | MR | Zbl

[27] Vlasov V. V., “O svoistvakh reshenii odnogo klassa funktsionalno-differentsialnykh uravnenii v gilbertovom prostranstve”, Nekotorye problemy matematiki v zadachakh fiziki i tekhniki, Mezhduvedomstvennyi sbornik nauchnykh trudov, MFTI, M., 1992, 26–36

[28] Vlasov V. V., “O nekotorykh svoistvakh reshenii lineinykh differentsialnykh uravnenii s posledeistviem v gilbertovom prostranstve”, Izv. vuzov. Mat., 1993, no. 5, 24–35 | MR | Zbl

[29] Vlasov V. V., “O svoistvakh reshenii odnogo klassa funktsionalno-differentsialnykh uravnenii i nekotorykh spektralnykh voprosakh”, Usp. mat. nauk, 48:4 (1993), 205

[30] Vlasov V. V., “Ob odnom klasse lineinykh differentsialnykh uravnenii s posledeistviem v gilbertovom prostranstve”, Usp. mat. nauk, 48:6 (1993), 147–148 | MR | Zbl

[31] Vlasov V. V., “O razreshimosti odnogo klassa differentsialnykh uravnenii s otklonyayuschimsya argumentom v gilbertovom prostranstve”, Izv. vuzov. Mat., 1994, no. 6, 28–38 | MR | Zbl

[32] Vlasov V. V., “O nekotorykh svoistvakh reshenii funktsionalno-differentsialnykh uravnenii v gilbertovom prostranstve”, Usp. mat. nauk, 49:3 (1994), 175–176 | MR | Zbl

[33] Vlasov V. V., “O razreshimosti i svoistvakh reshenii funktsionalno-differentsialnykh uravnenii v gilbertovom prostranstve”, Mat. sb., 186:8 (1995), 67–92 | MR | Zbl

[34] Vlasov V. V., “Korrektnaya razreshimost odnogo klassa differentsialnykh uravnenii s otklonyayuschimsya argumentom v gilbertovom prostranstve”, Izv. vuzov. Mat., 1996, no. 1, 22–35 | MR | Zbl

[35] Vlasov V. V., “Nekotorye svoistva sistemy elementarnykh reshenii differentsialno-raznostnykh uravnenii”, Usp. mat. nauk, 51:1 (1996), 143–144 | MR | Zbl

[36] Vlasov V. V., “Ob odnom klasse funktsionalno-differentsialnykh uravnenii s zapazdyvayuschim argumentom v gilbertovom prostranstve”, Mat. zametki, 62:5 (1997), 782–786 | MR | Zbl

[37] Vlasov V. V., “O razreshimosti i otsenkakh reshenii funktsionalno-differentsialnykh uravnenii v prostranstvakh Soboleva”, Tr. Mat. in-ta im. V. A. Steklova, 227, Nauka, M., 1999, 109–121 | MR | Zbl

[38] Vlasov V. V., “Ob odnom klasse differentsialno-raznostnykh uravnenii neitralnogo tipa”, Izv. vuzov. Mat., 1999, no. 2, 20–29 | MR | Zbl

[39] Vlasov V. V., “Ob otsenkakh reshenii differentsialno-raznostnykh uravnenii neitralnogo tipa”, Izv. vuzov. Mat., 2000, no. 4, 14–22 | MR | Zbl

[40] Vlasov V. V., “O svoistvakh sistemy eksponentsialnykh reshenii differentsialno-raznostnykh uravnenii v prostranstvakh Soboleva”, Izv. vuzov. Mat., 2001, no. 6, 23–29 | MR | Zbl

[41] Vlasov V. V., “O bazisnosti eksponentsialnykh reshenii funktsionalno-differentsialnykh uravnenii v prostranstvakh Soboleva”, Dokl. RAN, 381:3 (2001), 302–304 | MR | Zbl

[42] Vlasov V. V., “O bazisnosti semeistva eksponentsialnykh reshenii differentsialno-raznostnykh uravnenii”, Izv. vuzov. Mat., 2002, no. 6, 7–13 | MR | Zbl

[43] Vlasov V. V., “O korrektnoi razreshimosti abstraktnykh parabolicheskikh uravnenii s posledeistviem”, Dokl. RAN, 415:2 (2007), 151–154 | MR | Zbl

[44] Vlasov V. V., Ivanov S. A., “Bazisnost i otsenki reshenii uravnenii s posledeistviem v shkale prostranstv Soboleva”, Usp. mat. nauk, 56:3 (2001), 151–152 | MR | Zbl

[45] Vlasov V. V., Ivanov S. A., “Otsenki reshenii uravnenii s posledeistviem v prostranstvakh Soboleva i bazis iz razdelennykh raznostei”, Mat. zametki, 72:2 (2002), 303–306 | MR | Zbl

[46] Vlasov V. V., Ivanov S. A., “Otsenki reshenii uravnenii s posledeistviem v shkale prostranstv Soboleva i bazis iz razdelennykh raznostei”, Algebra i Analiz, 15:4 (2003), 115–141 | MR | Zbl

[47] Vlasov V. V., Ivanov S. A., “Ob otsenkakh reshenii funktsionalno-differentsialnykh uravnenii neitralnogo tipa v prostranstvakh Soboleva”, Dokl. RAN, 396:4 (2004), 443–445 | MR | Zbl

[48] Vlasov V. V., Ivanov S. A., “Otsenki reshenii neodnorodnykh differentsialno-raznostnykh uravnenii neitralnogo tipa”, Izv. vuzov. Mat., 2006, no. 3, 24–30 | MR | Zbl

[49] Vlasov V. V., Ivanov S. A., “O tochnykh otsenkakh differentsialno-raznostnykh uravnenii neitralnogo tipa”, Dokl. RAN, 406:5 (2006), 583–585 | MR | Zbl

[50] Vlasov V. V., Ivanov S. A., “Tochnye otsenki reshenii sistem uravnenii s posledeistviem”, Algebra i Analiz, 20:2 (2008), 43–69 | MR

[51] Vlasov V. V., Kurkina A. V., “Ob asimptoticheskom povedenii reshenii sistem funktsionalno-differentsialnykh uravnenii neitralnogo tipa”, Dokl. RAN, 402:4 (2005), 445–447 | MR

[52] Vlasov V. V., Malygina V. V., “K voprosu o korrektnoi razreshimosti lineinykh differentsialnykh uravnenii s posledeistviem v gilbertovykh prostranstvakh”, Differ. uravn., 28:5 (1992), 901–903 | MR | Zbl

[53] Vlasov V. V., Malygina V. V., “O korrektnoi razreshimosti nachalno-kraevoi zadachi dlya odnogo klassa integrodifferentsialnykh uravnenii”, Kraevye zadachi, Perm. politekh. in-t, Perm, 1989, 103–106 | MR

[54] Vlasov V. V., Medvedev D. A., “Otsenki reshenii differentsialno-raznostnykh uravnenii neitralnogo tipa”, Dokl. RAN, 389:2 (2003), 156–158 | MR | Zbl

[55] Vlasov V. V., Medvedev D. A., “Ob otsenkakh reshenii differentsialnykh uravnenii s zapazdyvayuschim argumentom”, Izv. vuzov. Mat., 2004, no. 6, 21–29 | MR | Zbl

[56] Vlasov V. V., Medvedev D. A., “Ob asimptoticheskikh svoistvakh reshenii funktsionalno-differentsialnykh uravnenii neitralnogo tipa”, Sovr. mat. Fundam. napr., 15, 2006, 112–125 | MR

[57] Vlasov V. V., Sakbaev V. Zh., “Korrektnaya razreshimost nekotorykh funktsionalno-differentsialnykh uravnenii v prostranstvakh Soboleva”, Mat. zametki, 68:6 (2000), 794–797 | MR | Zbl

[58] Vlasov V. V., Sakbaev V. Zh., “O korrektnoi razreshimosti v shkale prostranstv Soboleva nekotorykh differentsialno-raznostnykh uravnenii”, Differ. uravn., 37:9 (2001), 1194–1202 | MR | Zbl

[59] Vlasov V. V., Sakbaev V. Zh., “Korrektnaya razreshimost differentsialnykh uravnenii s posledeistviem v shkale prostranstv Soboleva”, Izv. vuzov. Mat., 2003, no. 4, 8–16 | MR | Zbl

[60] Vlasov V. V., Shmatov K. I., “Korrektnaya razreshimost uravnenii giperbolicheskogo tipa s zapazdyvaniem v gilbertovom prostranstve”, Tr. Mat. in-ta im. V. A. Steklova, 243, Nauka, M., 2003, 127–137 | MR | Zbl

[61] Gasymov M. G., “O kratnoi polnote chasti sobstvennykh i prisoedinennykh vektorov polinomialnykh puchkov”, Izv. AN ArmSSR. Ser. mat., 6:2–3 (1971), 131–147 | MR | Zbl

[62] Gokhberg I. Ts., Krein M. G., “Sistemy integralnykh uravnenii s yadrami, zavisyaschimi ot raznosti argumentov”, Usp. mat. nauk, 13:2 (1958), 3–72 | MR | Zbl

[63] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 | MR

[64] Gokhberg I. Ts., Sigal E. I., “Operatornoe obobschenie teoremy o logarifmicheskom vychete i teoremy Rushe”, Mat. sb., 84:4 (1971), 607–629 | MR | Zbl

[65] Gromova P. S., Ustoichivost reshenii lineinykh i kvazilineinykh differentsialno-raznostnykh uravnenii neitralnogo tipa v osobykh kriticheskikh sluchayakh, Diss. $\dots$ kand. fiz.-matem. nauk, M., 1967

[66] Gromova P. S., “Ustoichivost reshenii lineinykh differentsialno-raznostnykh uravnenii $n$-go poryadka v sverkhkriticheskom sluchae”, Tr. semin. po teorii differents. uravnenii s otklonyayusch. argumentom. Un-t druzhby narodov, 1975, no. 9, 31–38 | MR

[67] Gromova P. S., “Usloviya nalichiya u kvazipolinomov beskonechnykh tsepochek nulei, neogranichenno priblizhayuschikhsya k mnimoi osi”, Tr. semin. po teorii differents. uravnenii s otklonyayusch. argumentom. Un-t druzhby narodov, 1977, no. 10, 69–78

[68] Gromova P. S., Zverkin A. M., “O trigonometricheskikh ryadakh, summoi kotorykh yavlyaetsya nepreryvnaya neogranichennaya na chislovoi osi funktsiya – reshenie uravneniya s otklonyayuschimsya argumentom”, Differ. uravn., 4:10 (1968), 1174–1784 | MR

[69] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR

[70] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, IL, M., 1962

[71] Evgrafov E. A., Asimptoticheskie otsenki i tselye funktsii, Nauka, M., 1979 | MR | Zbl

[72] Zhdanovich V. F., “Formuly dlya nulei polinomov Dirikhle i kvazipolinomov”, Dokl. AN SSSR, 135:5 (1960), 1046–1049 | Zbl

[73] Zverkin A. M., “Ob odnom isklyuchitelnom sluchae raspolozheniya kornei kvazipolinomov”, Tr. semin. po teorii differents. uravnenii s otklonyayusch. argumentom. Un-t Druzhby narodov, 1963, no. 11, 238–243 | MR

[74] Zverkin A. M., “Razlozhenie v ryad reshenii lineinykh differentsialno-raznostnykh uravnenii. 1. Kvazipolinomy”, Tr. semin. po teorii differents. uravnenii s otklonyayusch. argumentom. Un-t Druzhby narodov, 1965, no. 5, 3–37 | MR

[75] Zverkin A. M., “Razlozhenie v ryad reshenii lineinykh differentsialno-raznostnykh uravnenii. 2. Razlozhenie reshenii v ryad”, Tr. semin. po teorii differents. uravnenii s otklonyayusch. argumentom. Un-t Druzhby narodov, 1967, no. 4, 3–51 | MR

[76] Zubov V. I., “K teorii lineinykh statsionarnykh sistem s zapazdyvayuschim argumentom”, Izv. vuzov. Mat., 1958, no. 6, 86–95 | MR | Zbl

[77] Zubov V. I., Teoriya upravlyaemogo dvizheniya, Uch. posobie, Izd-vo LGU, L., 1980 | Zbl

[78] Ilin V. A., “Neobkhodimye i dostatochnye usloviya bazisnosti v $L_p$ i ravnoskhodimosti s trigonometricheskim ryadom spektralnykh razlozhenii po sisteme eksponent”, Dokl. AN SSSR, 273:4 (1983), 789–793 | MR

[79] Kamenskii G. A., “K obschei teorii uravnenii s otklonyayuschimsya argumentom”, Dokl. AN SSSR, 120:4 (1958), 697–700 | MR | Zbl

[80] Kamenskii G. A., Skubachevskii A. L., Lineinye kraevye zadachi dlya differentsialno-raznostnykh uravnenii, Izd-vo MAI, M., 1992 | MR | Zbl

[81] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[82] Keldysh M. V., “O polnote sobstvennykh funktsii nekotorykh klassov nesamosopryazhennykh lineinykh operatorov”, Usp. mat. nauk, 26:4 (1971), 15–41 | MR | Zbl

[83] Kiryanen A. I., Ustoichivost sistem s posledeistviem i ikh prilozheniya, Izd-vo S.-Peterb. un-ta, SPb., 1994 | MR

[84] Kolmanovskii V. B., Nosov V. R., Ustoichivost i periodicheskie rezhimy reguliruemykh sistem s posledeistviem, Nauka, M., 1981 | MR | Zbl

[85] Kolmanovskii V. B., Nosov V. R., “Sistemy s posledeistviem neitralnogo tipa”, Avtom. telemekh., 1984, no. 1, 5–35 | MR | Zbl

[86] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi i uglovymi tochkami”, Tr. Mosk. Mat. o-va, 16, URSS, M., 1967, 209–292

[87] Kolpaschikov V. A., Shnip A. I., “K termodinamicheskoi teorii lineinogo provodnika s pamyatyu”, Problemy teplo- i massoperenosa, Sbornik nauchnykh trudov, Nauka i tekhnika, Minsk, 1976, 102–123

[88] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968 | MR

[89] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR

[90] Kurbatov V. G., Lineinye differentsialno-raznostnye uravneniya, Izd-vo VGU, Voronezh, 1990 | MR | Zbl

[91] Kurbatov V. G., “O razreshimosti otnositelno proizvodnoi ustoichivogo funktsionalno-differentsialnogo uravneniya”, Ukr. mat. zh., 34:1 (1982), 103–106 | MR | Zbl

[92] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[93] Levin B. Ya., “O bazisakh pokazatelnykh funktsii v $L_2$”, Zap. Kharkovsk. Mat. o-va, 27:4 (1961), 39–48

[94] Levin B. Ya., “Interpolyatsiya tselymi funktsiyami eksponentsialnogo tipa”, Tr. Fiz.-tekhn. in-ta nizkikh temperatur AN USSR, 1962, no. 1, 136–146 | MR

[95] Leontev A. F., “Differentsialno-raznostnye uravneniya”, Mat. sb., 24:3 (1949), 347–374 | MR | Zbl

[96] Leontev A. F., “Reshenie obobschennogo uravneniya svertki”, Izv. AN SSSR. Ser. mat., 43:2 (1979), 342–366 | MR | Zbl

[97] Lesnykh A. A., “Otsenki reshenii zapazdyvayuschikh uravnenii s peremennymi koeffitsientami”, Fundam. prikl. mat., 12:5 (2006), 83–93 | MR

[98] Lesnykh A. A., “Otsenki reshenii differentsialno-raznostnykh uravnenii neitralnogo tipa”, Mat. zametki, 81:4 (2007), 569–585 | MR | Zbl

[99] Lesnykh A. A., “Otsenki reshenii neodnorodnykh neitralnykh uravnenii”, Tr. KROMSh, Tavricheskii un-t, Simferopol, 2007, 14–21

[100] Lidskii V. B., “O summiruemocti ryadov po glavnym vektoram nesamosopryazhennykh operatorov”, Tr. Mosk. mat. o-va, 11, URSS, M., 1962, 3–35 | MR

[101] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[102] Luzhina L. M., “Regulyarnye spektralnye zadachi v prostranstve vektor-funktsii”, Vestn. Mosk. un-ta. Ser. 1. Mat. mekh., 1988, no. 1, 31–35 | MR | Zbl

[103] Lykov A. V., “Nekotorye problemnye voprosy teorii teplomassoperenosa”, Problemy teplo- i massoperenosa, Sbornik nauchnykh trudov, Nauka i tekhnika, Minsk, 1976, 9–82

[104] Lyubich Yu. I., “O sobstvennykh i prisoedinenykh funktsiyakh operatora differentsirovaniya”, Izv. vuzov. Mat., 1959, no. 4, 94–103 | Zbl

[105] Mazya V. G., Plamenevskii B. A., “Ob asimptoticheskom povedenii reshenii differentsialnykh uravnenii v gilbertovom prostranstve”, Izv. AN SSSR. Ser. mat., 36:5 (1972), 1080–1133 | MR | Zbl

[106] Markus A. S., Vvedenie v pektralnuyu teoriyu polinomialnykh operatornykh puchkov, Shtiintsa, Kishinev, 1986 | MR | Zbl

[107] Medvedev D. A., “Asimptoticheskoe povedenie reshenii uravnenii s posledeistviem v gilbertovom prostranstve”, Usp. mat. nauk, 62:1 (2007), 201–202 | MR

[108] Medvedev D. A., “Asimptoticheskoe povedenie reshenii uravnenii s zapazdyvayuschim argumentom v gilbertovom prostranstve”, Sovr. mat. Fundam. napr., 21, 2007, 83–92 | MR

[109] Miloslavskii A. I., “Ob ustoichivosti nekotorykh klassov evolyutsionnykh uravnenii”, Sib. mat. zh., 26:5 (1985), 118–132 | MR | Zbl

[110] Miloslavskii A. I., Spektralnye svoistva operatornogo puchka, voznikayuschego v vyazkouprugosti, Deponirovano v UkrNIKNTI, 1987

[111] Mirolyubov A. A., Soldatov M. A., Lineinye odnorodnye raznostnye uravneniya, Nauka, M., 1981 | MR | Zbl

[112] Mikhailov V. P., “O bazisakh Rissa v $L_2(0,1)$”, Dokl. AN SSSR, 144:5 (1962), 981–984

[113] Mikhlin S. G., Lineinye uravneniya v chastnykh proizvodnykh, Vysshaya shkola, M., 1977 | MR

[114] Molodenkov V. A., Khromov A. P., “Razlozhenie po sobstvennym funktsiyam kraevoi zadachi dlya operatora differentsirovaniya”, Differentsialnye uravneniya i vychislitelnaya matematika, T. 1, Saratov, 1972, 17–26 | MR | Zbl

[115] Myshkis A. D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972 | MR | Zbl

[116] Myshkis A. D., “O nekotorykh problemakh teorii differentsialnykh uravnenii s otklonyayuschimsya argumentom”, Usp. mat. nauk, 32:2 (1977), 173–202 | MR | Zbl

[117] Myshkis A. D., “Smeshannye funktsionalno-differentsialnye uravneniya”, Sovr. mat. Fundam. napr., 4, 2003, 5–120 | MR | Zbl

[118] Myshkis A. D., Elsgolts L. E., “Sostoyanie i problemy teorii differentsialnykh uravnenii s otklonyayuschimsya argumentom”, Usp. mat. nauk, 22:2 (1967), 21–57 | MR | Zbl

[119] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

[120] Nikolskii N. K., Lektsii ob operatore sdviga, Nauka, M., 1980 | MR

[121] Pavlov B. S., “Bazisnost sistemy eksponent i uslovie Makenkhaupta”, Dokl. AN SSSR, 247:1 (1979), 37–40 | MR | Zbl

[122] Pinni E., Obyknovennye differentsialno-raznostnye uravneniya, IL, M., 1961

[123] Radzievskii G. V., “O bazisnosti proizvodnykh tsepochek”, Izv. AN SSSR. Ser. mat., 39:5 (1975), 1182–1218 | MR | Zbl

[124] Radzievskii G. V., “Asimptotika raspredeleniya kharakteristicheskikh chisel operator-funktsii, analiticheskikh v ugle”, Mat. sb., 154:3 (1980), 396–420 | MR | Zbl

[125] Radzievskii G. V., “Zadacha o polnote kornevykh vektorov v spektralnoi teorii operator-funktsii”, Usp. mat. nauk, 37:2 (1982), 81–145 | MR | Zbl

[126] Sedletskii A. M., “O funktsiyakh, periodicheskikh v srednem”, Izv. AN SSSR. Ser. mat., 34:6 (1970), 1391–1415 | MR | Zbl

[127] Sedletskii A. M., “Periodicheskoe v srednem prodolzhenie nepreryvnykh funktsii s sokhraneniem gladkosti”, Dokl. AN SSSR, 212:2 (1973), 302–304

[128] Sedletskii A. M., “O polnote sistemy eksponent v prostranstvakh differentsiruemykh funktsii”, Tr. Mosk. energ. in-ta, 334 (1977), 98–103

[129] Sedletskii A. M., “Biortogonalnye razlozheniya funktsii v ryady eksponent na intervalakh veschestvennoi osi”, Usp. mat. nauk, 37:5 (1982), 51–95 | MR | Zbl

[130] Sedletskii A. M., “Prodolzhenie nazad reshenii odnorodnogo uravneniya svertki zapazdyvayuschego tipa”, Differ. uravn., 27:4 (1991), 709–711 | MR

[131] Sedletskii A. M., “Approksimativnye svoistva sistem eksponent v prostranstvakh Soboleva”, Vestn. Mosk. un-ta. Ser. 1. Mat., mekh., 1999, no. 6, 3–8 | MR

[132] Sedletskii A. M., “Analiticheskie preobrazovaniya Fure i eksponentsialnye approksimatsii. I”, Sovr. mat. Fundam. napr., 5, 2003, 3–152 ; “Аналитические преобразования Фурье и экспоненциальные аппроксимации. II”, 6, 3–162 | Zbl

[133] Sedletskii A. M., Klassy analiticheskikh preobrazovanii Fure i eksponentsialnye approksimatsii, Fizmatlit, M., 2005

[134] Skubachevskii A. L., Steblov G. M., “O spektre differentsialnykh operatorov s oblastyu opredeleniya, ne plotnoi v $L_2(0,1)$”, Dokl. AN SSSR, 321:6 (1991), 1158–1163 | MR

[135] Skubachevskii A. L., “Ellipticheskie zadachi s nelokalnymi usloviyami v blizi granitsy”, Mat. sb., 129(171):2 (1986), 279–302 | MR | Zbl

[136] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR | Zbl

[137] Tyshkevich V. A., Nekotorye voprosy teorii ustoichivosti funktsionalno-differentsialnykh uravnenii, Naukova Dumka, Kiev, 1981 | MR | Zbl

[138] Khan V., “Obzor teorii differentsialno-raznostnykh uravnenii s postoyannymi i peremennymi otkloneniyami”, Matematika, Sb. perev. inostr. statei, 5, no. 6, 1961, 73–98

[139] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984 | MR

[140] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, IL, M., 1962

[141] Khromov A. P., “Razlozhenie po sobstvennym funktsiyam obyknovennykh differentsialnykh operatorov v konechnom intervale”, Dokl. AN SSSR, 146:6 (1962), 1294–1297 | Zbl

[142] Khromov A. P., “Konechnomernye vozmuscheniya volterrovykh operatorov”, Sovr. mat. Fundam. napr., 10, 2004, 3–163 | MR | Zbl

[143] Sharkovskii A. N., Maistrenko Yu. L., Romanenko E. Yu., Raznostnye uravneniya i ikh prilozheniya, Naukova dumka, Kiev, 1986 | MR

[144] Shilov G. E., Matematicheskii analiz. Vtoroi spetsialnyi kurs, Nauka, M., 1965 | MR

[145] Shkalikov A. A., “O bazisnosti sobstvennykh funktsii obyknovennykh differentsialnykh operatorov s integralnymi kraevymi usloviyami”, Vestn. Mosk. un-ta. Ser. 1. Mat., mekh., 1982, no. 6, 12–21 | MR | Zbl

[146] Shkalikov A. A., “Nekotorye voprosy teorii polinomialnykh operatornykh puchkov”, Usp. mat. nauk, 38:3 (1983), 189–190 | MR | Zbl

[147] Shkalikov A. A., “Kraevye zadachi dlya obyknovennykh differentsialnykh uravnenii s parametrom v granichnykh usloviyakh”, Tr. semin. im. I. G. Petrovskogo, no. 9, Izd-vo Mosk. un-ta, M., 1983, 190–229 | MR

[148] Shkalikov A. A., “Ellipticheskie uravneniya v gilbertovom prostranstve i spektralnye zadachi, svyazannye s nimi”, Tr. semin. im. I. G. Petrovskogo, no. 14, Izd-vo Mosk. un-ta, M., 1989, 140–224

[149] Elsgolts E. L., Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M., 1964 | MR

[150] Agmon S., Nirenberg L., “Properties of solutions of ordinary differential equations in Banach spaces”, Commun. Pure Appl. Math., 16 (1963), 121–239 | DOI | MR | Zbl

[151] Bagirov L. A., Kondratyev V. A., “On the properties of generalized solutions of elliptic equations”, Russ. J. Math. Phys., 1:2 (1993), 139–164 | MR | Zbl

[152] Brumley W. E., “On the asymtotic behavior of solutions of differential-difference equations of neutral type”, J. Differ. Equations, 7 (1970), 175–188 | DOI | MR | Zbl

[153] Burns J. A., Herdman T. L., Stech H. W., “Linear functional differential equations as semigroups on product spaces”, SIAM J. Math. Anal., 14:1 (1983), 98–116 | DOI | MR | Zbl

[154] Datko R., “Uniform asymptotic stability of evolutionary processes in a Banach space”, SIAM J. Math. Anal., 3 (1973), 428–445 | DOI | MR

[155] Datko R., “Representation of solutions and stability of linear differential-difference equation in a Banach space”, J. Differ. Equations, 29:1 (1978), 105–166 | DOI | MR

[156] Davis P. L., “Hyperbolic integrodifferential equations”, Proc. Amer. Math. Soc., 47 (1975), 155–160 | DOI | MR | Zbl

[157] Davis P. L., “On the hyperbolicity of the equations of the linear theory of heat conduction for materials with memory”, SIAM J. Appl. Math., 30 (1976), 75–80 | DOI | MR | Zbl

[158] Delfour M. C., Manitius A., “The structural operator $F$ and its role in the theory of retarded systems. I”, J. Math. Anal. Appl., 73 (1980), 466–490 | DOI | MR | Zbl

[159] Delfour M. C., Manitius A., “The structural operator $F$ and its role in the theory of retarded systems. II”, J. Math. Anal. Appl., 74 (1980), 359–381 | DOI | MR | Zbl

[160] Desch W., Grimmer R., Shappacher W., “Wellposedness and wave propagation for a class of integrodifferential equations in Banach space”, J. Differ. Equations, 74 (1988), 391–411 | DOI | MR | Zbl

[161] Desch W., Miller R. K., “Exponential stabilization of Voltera integrodifferential equations in Hilbert space”, J. Differ. Equations, 70 (1987), 366–389 | DOI | MR | Zbl

[162] Di Blasio G., “Parabolic Volterra equations of convolution type”, J. Integral Equations Appl., 6 (1994), 479–508 | DOI | MR | Zbl

[163] Di Blasio G., Kunisch K., Sinestrari E., “$L^2$-regularity for parabolic partial integrodifferential equations with delays in the highest order derivatives”, J. Math. Anal. Appl., 102 (1984), 38–57 | DOI | MR | Zbl

[164] Di Blasio G., Kunisch K., Sinestrari E., “Stability for abstract linear functional differential equations”, Israel J. Math., 50:3 (1985), 231–263 | DOI | MR | Zbl

[165] Diekman O., van Gils S. A., Verduyn Lunel S., Walther H. O., Delay equations: Functional, complex, and nonlinear analysis, Springer-Verlag, New York, 1995 | MR | Zbl

[166] Driver R. D., Ordinary and delay differential equations, Springer-Verlag, New York, 1999 | MR

[167] Engel K-J., Nagel R., One-parameter semigroup for linear evolution equations, Springer-Verlag, New York, 2000 | MR

[168] Grimmer R. C., Kappel F., “Series expansions for resolvents of Volterra integrodifferential equations in Banach spaces”, SIAM J. Math. Anal., 15:3 (1984), 595–604 | DOI | MR | Zbl

[169] Grimmer R. C., Pritchard A. J., “Analytic resolvent operators for integral equations in Banach spaces”, J. Differ. Equations, 50 (1983), 234–259 | DOI | MR | Zbl

[170] Gurtin M. E., Pipkin A. C., “Theory of heat conduction with finite wave speed”, Arch. Rat. Mech. Anal., 31 (1968), 113–126 | DOI | MR | Zbl

[171] Hahn W., “Über Differential-Differenzengleichungen mit anomalen Zosungum”, Math. Ann., 133:3 (1957), 251–255 | DOI | MR | Zbl

[172] Hale J., Verduyn Lunel S., Introduction to the theory of functional differential equations, Springer-Verlag, New York, 1993

[173] Henry D., “Linear autonomous neutral functional differential equations”, J. Differ. Equations, 15 (1974), 106–128 | DOI | MR | Zbl

[174] Ito K., Kappel F., Turi J., “On well-posedness of singular neutral equations in the state space $C$”, J. Differ. Equations, 125 (1996), 40–72 | DOI | MR | Zbl

[175] Ivanov S. A., Kalton N., “Interpolation of subspaces and applications to exponential bases”, Algebra i Analiz, 13:2 (2001), 93–115 | MR

[176] Ivanov S., Pandolfi L., Heat equations with memory: lack of controllability to the rest, Rapporto interno, Politecnico di Torino, 2007, 35 pp.

[177] Kappel F., Kunisch K., “Invariance result for delay and Volterra equations in fractional order Sobolev spaces”, Trans. Amer. Math. Soc., 304:1 (1987), 1–51 | DOI | MR | Zbl

[178] Kappel F., Laplace-transform methods and linear autonomous functional differential equations, Reprint No 33, Math. Inst., University of Graz (Austria), 1984 | MR

[179] Kappel F., Kang pei Zhang, “Equivalence of functional-differential equations of neutral type and abstract Cauchy problem”, Monats. Math., 101 (1986), 115–133 | DOI | MR | Zbl

[180] Kolmanovsky V., Myshkis A., Introduction to the theory of functional differential equations, Kluwer, Dortmunt–Basel–New York, 1999

[181] Kolmanovskii V., Nosov V., Stability of functional differential equations, Academic Press, San Diego, 1986 | MR | Zbl

[182] Krall A. M., “The development of general differential operators and general differential boundary systems”, Rocky Mountain J. Math., 5:4 (1975), 493–542 | DOI | MR | Zbl

[183] Khrushchev S. V., Nikol'skii N. K., Pavlov B. S., “Unconditional bases of exponentials and reproducing kernels”, Complex analiysis and spectral theory, Lect. Notes Math., 864, Springer-Verlag, Berlin–Heidelberg, 1981, 214–335 | MR

[184] Kunish K., Mastinšek M., “Dual semigroups and structural operators for partial differential equations with unbounded operators acting on the delays”, Differ. Integral Equations, 3:4 (1990), 733–756 | MR

[185] Kunish K., Shappacher W., “Necessary conditions for partial differential equations with delay to generate $l_0$-semigroup”, J. Differ. Equations, 50 (1983), 49–79 | DOI | MR

[186] Levinson N., Gap and density theorems, Coll. Publ., 26, Amer. Math. Soc., New York, 1940 | MR | Zbl

[187] Levinson N., McCalla C., “Completeness and independence of the exponential of some functional differential equations”, Stud. Appl. Math., 53 (1974), 1–15 | MR

[188] Manitius A., “Completeness and F-completeness of eigenfunctions associated with retarded functional differential equations”, J. Differ. Equations, 35 (1980), 1–29 | DOI | MR | Zbl

[189] Medvedev D. A., Vlasov V. V., Wu J., “Solvability and structural properties of abstract neutral functional differential equations”, Funct. Differ. Equations, 15:3–4 (2008), 249–268 | MR

[190] Miller R. K., “Volterra integral equations in a Banach space”, Funkcialaj Ekvac., 18 (1975), 163–194 | MR

[191] Miller R. K., “An integrodifferencial equation for rigid heat conductors with memory”, J. Math. Anal. Appl., 66 (1978), 313–332 | DOI | MR | Zbl

[192] Miller R. K., Wheeler R. L., “Well-posedness and stability of linear Volterra integrodifferential equations in abstract spaces”, Funkcialaj Ekvac., 21 (1978), 279–305 | MR | Zbl

[193] Myshkis A. D., Vlasov V. V., “On an analogy between the classification of functional differential equations and partial differential equations”, Funct. Differ. Equations (to appear)

[194] Nakagiri S., “Structural properties of functional differential equations in Banach space”, Osaka J. Math., 25 (1988), 353–398 | MR | Zbl

[195] Nakagiri S., Yamomoto M., “Identifiability of linear retarded systems in Banach spaces”, Funkcialaj Ekvac., 31 (1988), 315–329 | MR | Zbl

[196] Nakagiri S., Yamomoto M., “Controlability and observability of linear retarded systems in Banach spaces”, Int. J. Control., 49 (1989), 1489–1504 | MR | Zbl

[197] Pandolfi L., “The controllability of the Gurtin–Pipkin equations: a cosine operator approach”, Appl. Math. Optim., 52 (2005), 143–165 | DOI | MR | Zbl

[198] Prüss J., “On linear Volterra equations of parabolic type in Banach spaces”, Trans. Amer. Math. Soc., 301:2 (1987), 691–721 | DOI | MR | Zbl

[199] Prüss J., “Bounded solutions of Volterra equations”, SIAM J. Math. Anal., 19:1 (1988), 133–149 | DOI | MR | Zbl

[200] Prüss J., Evolutionary integral equations and applications, Monogr. Math., 87, Birkhäuser, Basel, 1993 | MR | Zbl

[201] Rabath R., Sklyar G., Resounenko A., “Generalized Riesz basis property in the analysis of neutral type systems”, C. R. Acad. Sci. Paris, 1337 (2003), 19–24 | MR

[202] Russel D., “On exponential bases for the Sobolev spaces over an interval”, J. Math. Anal. Appl., 87:2 (1982), 528–550 | DOI | MR | Zbl

[203] Skubachevskii A. L., Elliptic functional differential equations and applications, Birkhäuser, Basel, 1997 | MR | Zbl

[204] Staffans O. J., “On neutral functional differential equations in fading memory space”, J. Differ. Equations, 50:2 (1983), 183–217 | DOI | MR | Zbl

[205] Staffans O. J., “Some well-posed functional equations which generate semigroups”, J. Differ. Equations, 58:2 (1985), 157–191 | DOI | MR | Zbl

[206] Talmor G., Turi J., “Neutral equations and associated semigroups”, J. Differ. Equations, 116 (1995), 59–87 | DOI | MR

[207] Tanabe H., “Structural operators for linear delay-differential equations in Hilbert space”, Proc. Japan. Acad. Ser. A Math. Sci., 64:8 (1988), 265–266 | DOI | MR | Zbl

[208] Travis C. C., Webb G. F., “Partial differential equations with deviating arguments in the time variable”, J. Math. Anal. Appl., 56:2 (1976), 397–409 | DOI | MR | Zbl

[209] Travis C. C., Webb G. F., “Existense, stability and completness in $\alpha$-norm for partial functional differential equations”, Trans. Amer. Math. Soc., 240 (1978), 129–143 | DOI | MR | Zbl

[210] Verblunsky S., “On an expansion in exponential series”, Quart. J. Math. Oxford Ser. (2), 7 (1956), 231–240 | DOI | MR | Zbl

[211] Verduyn Lunel S. M., “Series expansions and small solutions for Volterra equations of convolution type”, J. Differ. Equations, 85:1 (1990), 17–53 | DOI | MR | Zbl

[212] Verduyn Lunel S. M., “The closure of the generalised eigenspace of a class of infinitesimal generators”, Proc. Roy. Soc. Edinburg. Sec. A, 117:1–2 (1991), 171–192 | MR | Zbl

[213] Verduyn Lunel S. M., “Small solutions and completness for linear functional differential equations”, Contemp. Math., 129 (1992), 127–152 | MR | Zbl

[214] Verduyn Lunel S. M., Yakubovich D. V., “A functional model approach to linear neutral functional difference equations”, Integr. Equations Oper. Theory, 27 (1997), 347–378 | DOI | MR | Zbl

[215] Vlasov V. V., “On spectral problems arising in the theory of functional differential equations”, Funct. Differ. Equations, 8:3–4 (2001), 435–446 | MR | Zbl

[216] Vlasov V. V., Medvedev D. A., “Estimates of solutions to differential-difference equations of the neutral type”, Funct. Differ. Equations, 9:3–4 (2002), 423–435 | MR | Zbl

[217] Vlasov V. V., Medvedev D. A., “On asymptotic behavior and estimates of solutions to neutral equations”, Funct. Differ. Equations, 13:2 (2006), 207–223 | MR | Zbl

[218] Vlasov V. V., Wu J., “Sharp estimates of solutions to neutral equations in Sobolev spaces”, Funct. Differ. Equations, 12:3–4 (2005), 437–461 | MR | Zbl

[219] Vlasov V. V., Wu J., “Solvability and spectral analysis of abstract hyperbolic equations with delay”, Funct. Differ. Equations (to appear)

[220] Wu J., “Semigroup and integral form of class of partial differential equations with infinite delay”, Differ. Integr. Equations, 4:6 (1991), 1325–1351 | MR | Zbl

[221] Wu J., Theory and applications of partial functional differential equations, Appl. Math. Sci., 119, Springer-Verlag, New York, 1996 | MR