Sobolev space estimates for solutions of equations with retardation, and a~basis built from divided differences
Algebra i analiz, Tome 15 (2003) no. 4, pp. 115-141.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{AA_2003_15_4_a3,
     author = {V. V. Vlasov and S. A. Ivanov},
     title = {Sobolev space estimates for solutions of equations with retardation, and a~basis built from divided differences},
     journal = {Algebra i analiz},
     pages = {115--141},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2003_15_4_a3/}
}
TY  - JOUR
AU  - V. V. Vlasov
AU  - S. A. Ivanov
TI  - Sobolev space estimates for solutions of equations with retardation, and a~basis built from divided differences
JO  - Algebra i analiz
PY  - 2003
SP  - 115
EP  - 141
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2003_15_4_a3/
LA  - ru
ID  - AA_2003_15_4_a3
ER  - 
%0 Journal Article
%A V. V. Vlasov
%A S. A. Ivanov
%T Sobolev space estimates for solutions of equations with retardation, and a~basis built from divided differences
%J Algebra i analiz
%D 2003
%P 115-141
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2003_15_4_a3/
%G ru
%F AA_2003_15_4_a3
V. V. Vlasov; S. A. Ivanov. Sobolev space estimates for solutions of equations with retardation, and a~basis built from divided differences. Algebra i analiz, Tome 15 (2003) no. 4, pp. 115-141. http://geodesic.mathdoc.fr/item/AA_2003_15_4_a3/

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

[2] Vasyunin V. I., “Bezuslovno skhodyaschiesya spektralnye razlozheniya i zadachi interpolyatsii”, Tr. Mat. in-ta AN SSSR, 130, 1978, 5–49 | MR | Zbl

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

[4] Khrushchev S. V., Nikol'skiĭ N. K., Pavlov B. S., “Unconditional bases of exponentials nd of reproducing kernels”, Complex Analysis and Spectral Theory (Leningrad, 1979/1980), Lecture Notes in Math., 864, Springer-Verlag, Berlin–New York, 1981, 214–335

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

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

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

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

[9] Vlasov V. V., Ivanov S. A., “Bazisnost i otsenki reshenii uravnenii s posledeistviem v shkale prostranstv Soboleva”, Uspekhi mat. nauk, 56:3(339) (2001), 151–152 | MR | Zbl

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

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

[12] Shilov G. E., Matematicheskii analiz, Vtoroi spetskurs, Nauka, M., 1965

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

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

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

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

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

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

[19] 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

[20] Verduyn Lunel S. M., Yakubovich D. V., “A functional model approach to linear neutral functional-differential equations”, Integral Equations Operator Theory, 27:3 (1997), 347–378 | DOI | MR | Zbl

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

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

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

[24] Levin B. Ya., “O bazisakh pokazatelnykh funktsii v $L^2$”, Uchen. zap. Kharkov. un-ta, 115 (1961), 39–48

[25] Shkalikov A. A., “Kraevye zadachi dlya obyknovennykh differentsialnykh uravnenii s parametrom v granichnykh usloviyakh”, Tr. semin. im. I. G. Petrovskogo, 9, 1983, 190–229 | MR | Zbl

[26] Sedletskii A. M., “Biortogonalnye razlozheniya funktsii v ryady eksponent na intervalakh veschestvennoi osi”, Uspekhi mat. nauk, 37:5(227) (1982), 51–95 | MR

[27] 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

[28] Gromova P. S., Zverkin A. M., “O trigonometricheskikh ryadakh, summoi kotorykh yavlyaetsya nepreryvnaya neogranichennaya na chislovoi osi funktsiya – reshenie uravneniya s otklonyayuschimsya argumentom”, Differents. uravneniya, 4:10 (1968), 1774–1784 | MR | Zbl