Slowly varying on infinity semigroups of operators
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 3-14.

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

We study the asymptotical behavior of bounded semigroups of linear operators in Banach spaces. The results are tightly connected with research of stabilisation of solutions of parabolic equations when time tends to infinity. The traditional condition of existence of an average of initial functions is not required.
Keywords: slowly varying functions, semigroups of linear operators, Beurling spectrum, harmonic analysis.
@article{IVM_2014_7_a0,
     author = {A. G. Baskakov and N. S. Kaluzhina and D. M. Polyakov},
     title = {Slowly varying on infinity semigroups of operators},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--14},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_7_a0/}
}
TY  - JOUR
AU  - A. G. Baskakov
AU  - N. S. Kaluzhina
AU  - D. M. Polyakov
TI  - Slowly varying on infinity semigroups of operators
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 3
EP  - 14
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_7_a0/
LA  - ru
ID  - IVM_2014_7_a0
ER  - 
%0 Journal Article
%A A. G. Baskakov
%A N. S. Kaluzhina
%A D. M. Polyakov
%T Slowly varying on infinity semigroups of operators
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 3-14
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_7_a0/
%G ru
%F IVM_2014_7_a0
A. G. Baskakov; N. S. Kaluzhina; D. M. Polyakov. Slowly varying on infinity semigroups of operators. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2014_7_a0/

[1] Tikhonov A. N., “Ob uravnenii teploprovodnosti dlya neskolkikh peremennykh”, Byull. MGU. Matem. mekhan., 1938, no. 1(9), 1–49

[2] Kolmogorov A. N., Petrovskii I. G., Piskunov N. S., “Issledovanie uravneniya diffuzii, soedinennoi s vozrastaniem kolichestva veschestva, i ego primenenie k odnoi biologicheskoi probleme”, Byull. MGU. Matem. mekhan., 1937, no. 1(6), 1–26

[3] Ilin A. M., “O povedenii resheniya zadachi Koshi dlya parabolicheskogo uravneniya pri neogranichennom vozrastanii vremeni”, UMN, 16:2 (1961), 115–121 | MR | Zbl

[4] Repnikov V. D., Eidelman S. D., “Neobkhodimye i dostatochnye usloviya stabilizatsii resheniya zadachi Koshi dlya parabolicheskogo uravneniya”, DAN SSSR, 167:2 (1966), 298–301 | MR | Zbl

[5] Denisov V. N., Repnikov V. D., “O stabilizatsii resheniya zadachi Koshi dlya parabolicheskikh uravnenii”, Differents. uravneniya, 20:1 (1984), 20–41 | MR | Zbl

[6] Guschin A. K., Mikhailov V. P., Mikhailov Yu. A., “O ravnomernoi stabilizatsii resheniya vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka”, Matem. sb., 128(170):2 (1985), 147–168 | MR | Zbl

[7] Mukminov F. Kh., “O ravnomernoi stabilizatsii reshenii pervoi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 101(143):4 (1976), 459–499

[8] Denisov V. N., “O povedenii reshenii parabolicheskikh uravnenii pri bolshikh znacheniyakh vremeni”, UMN, 60:4 (2005), 145–212 | DOI | MR | Zbl

[9] Baskakov A. G., Kaluzhina N. S., “Teorema Berlinga dlya funktsii s suschestvennym spektrom iz odnorodnykh prostranstv i stabilizatsiya reshenii parabolicheskikh uravnenii”, Matem. zametki, 92:5 (2012), 643–661 | DOI | Zbl

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

[11] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, In. lit., M., 1962 | MR

[12] Khyuitt E., Ross K. A., Abstraktnyi garmonicheskii analiz, v. 2, Struktura i analiz na kompaktnykh gruppakh. Analiz na lokalno kompaktnykh abelevykh gruppakh, Nauka, M., 1975

[13] Baskakov A. G., “Teoriya predstavlenii banakhovykh algebr, abelevykh grupp i polugrupp v spektralnom analize lineinykh operatorov”, SMFN, 9, MAI, 2004, 3–151 | MR | Zbl

[14] Baskakov A. G., Krishtal I. A., “Garmonicheskii analiz kauzalnykh operatorov i ikh spektralnye svoistva”, Izv. RAN. Ser. matem., 69:3 (2005), 3–54 | DOI | MR | Zbl

[15] Baskakov A. G., Garmonicheskii analiz lineinykh operatorov, Izd-vo VGU, Voronezh, 1987 | MR | Zbl

[16] Baskakov A. G., “Spektralnye kriterii pochti periodichnosti reshenii funktsionalnykh uravnenii”, Matem. zametki, 24:2 (1978), 195–206 | MR | Zbl

[17] Baskakov A. G., Sintyaeva K. A., “O neravenstvakh Bora–Favara dlya operatorov”, Izv. vuzov. Matem., 2009, no. 12, 14–21 | MR | Zbl

[18] Baskakov A. G., “Polugruppy raznostnykh operatorov v spektralnom analize lineinykh differentsialnykh operatorov”, Funkts. analiz i ego pril., 30:3 (1996), 1–11 | DOI | MR | Zbl

[19] Baskakov A. G., “Lineinye differentsialnye operatory s neogranichennymi operatornymi koeffitsientami i polugruppy raznostnykh operatorov”, Matem. zametki, 59:6 (1996), 811–820 | DOI | MR | Zbl

[20] Baskakov A. G., “Spektralnyi analiz differentsialnykh operatorov s neogranichennymi operatornymi koeffitsientami, raznostnye otnosheniya i polugruppy raznostnykh otnoshenii”, Izv. RAN. Ser. matem., 73:2 (2009), 3–68 | DOI | MR | Zbl

[21] Khenri D., Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Mir, M., 1985 | MR

[22] Baskakov A. G., “Ob obschikh ergodicheskikh teoremakh v banakhovykh modulyakh”, Funkts. analiz i ego pril., 14:3 (1980), 63–64 | MR | Zbl

[23] Baskakov A. G., “Operatornye ergodicheskie teoremy i dopolnyaemye podprostranstva banakhovykh prostranstv”, Izv. vuzov. Matem., 1988, no. 11, 3–11 | MR | Zbl

[24] Repnikov V. D., “O ravnomernoi stabilizatsii resheniya zadachi Koshi dlya parabolicheskikh uravnenii”, DAN SSSR, 157:3 (1964), 532–535 | MR | Zbl

[25] Baskakov A. G., “O korrektnosti lineinykh differentsialnykh operatorov”, Matem. sb., 190:3 (1999), 3–28 | DOI | MR | Zbl

[26] Baskakov A. G., “Lineinye otnosheniya kak generatory polugrupp operatorov”, Matem. zametki, 84:2 (2008), 175–192 | DOI | MR | Zbl