Geodesic
Almost periodic at infinity solutions of difference equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 38-46.

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We consider a new class of functions almost periodic at infinity defined by using the subspace of functions that integrally decrease at infinity. We propose four definitions of functions almost periodic at infinity and prove their equivalence. Also, we obtain spectral criteria of almost periodicity at infinity of bounded solutions of systems of linear difference equations and their asymptotic representation.
Keywords: function almost periodic at infinity, function slowly changing at infinity, function integrally decreasing at infinity, difference equation. 
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I. A. Vysotskaya. Almost periodic at infinity solutions of difference equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 38-46. http://geodesic.mathdoc.fr/item/INTO_2019_171_a2/

[1] Baskakov A. G., Strukova I. I., Trishina I. A., “Pochti periodicheskie na beskonechnosti resheniya differentsialnykh uravnenii s neogranichennymi operatornymi koeffitsientami”, Sib. mat. zh., 59:2 (348) (2018), 293–308 | MR | Zbl

[2] Baskakov A. G., “Teoriya predstavlenii banakhovykh algebr, abelevykh grupp i polugrupp v spektralnom analize lineinykh operatorov”, Sovr. mat. Fundam. napravl., 9 (2004), 3–151 | Zbl

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

[4] Baskakov A. G., Kaluzhina N. S., Polyakov D. M., “Medlenno menyayuschiesya na beskonechnosti polugruppy operatorov”, Izv. vuzov. Mat., 2014, no. 7, 3–14 | Zbl

[5] Baskakov A. G., “Spektralnye kriterii pochti periodichnosti reshenii funktsionalnykh uravnenii”, Mat. zametki., 24:2 (1978), 195–206

[6] Gelfand I. M., Raikov D. A., Shilov G. E., Kommutativnye normirovannye koltsa, Fizmatgiz, M., 1967

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

[8] Levitan B. M., Pochti periodicheskie funktsii, Gostekhizdat, M., 1953 | MR

[9] fon Neiman Dzh., Izbrannye trudy po funktsionalnomu analizu, Nauka, M., 1987

[10] Ryzhkova A. A., Trishina I. A., “O pochti periodicheskikh na beskonechnosti resheniyakh raznostnykh uravnenii”, Izv. Saratov. un-ta. Ser. Mat. Mekh. Inform., 15:1 (2015), 45–49 | Zbl

[11] Ryzhkova A. A., Trishina I. A., “O periodicheskikh na beskonechnosti funktsiyakh”, Nauch. ved. Belgorod. gos. un-ta. Ser. Mat. Fiz., 36:19 (2014), 71–75

[12] Sobolev S. L., “O pochti periodichnosti reshenii volnovogo uravneniya”, Dokl. AN SSSR., 49:1 (1945), 12–15 | Zbl

[13] Trishina I. A., “Pochti periodicheskie na beskonechnosti funktsii otnositelno podprostranstva integralno ubyvayuschikh na beskonechnosti funktsii”, Izv. Saratov. un-ta. Ser. Mat. Mekh. Inform., 17:4 (2017), 402–418 | MR | Zbl

[14] Trishina I. A., “Medlenno menyayuschiesya na beskonechnosti funktsii”, Vestn. Voronezh. gos. un-ta. Ser. Fiz. Mat., 2017, no. 4, 134–144 | MR | Zbl

[15] Amerio L., Prouse G., Almost Periodic Functions and Functional Equations, Springer-Verlag, New York, 1971 | MR

[16] Arendt W., Batty C. J. K., “Asymptotic almost periodic solutions of inhomogeneous Cauchy problems on the half-line”, Bull. London Math. Soc., 31:3 (1991), 291–304 | DOI | MR

[17] Bochner S., von Neuman J., “On compact solution of operational differentional equations”, Ann. Math., 36 (1935), 435–447 | DOI | MR