Abstract:
The new class of functions almost periodic at infinity is defined using the subspace of functions with integrals decreasing at infinity. We obtain spectral criteria for almost periodicity at infinity of bounded solutions to differential equations with unbounded operator coefficients. For the new class of asymptotically finite operator semigroups we prove the almost periodicity at infinity of their orbits.
Keywords:
functions almost periodic at infinity, Banach modules, differential equations with unbounded operator coefficients, function spectrum, operator spectrum, operator semigroups.
The first author was supported by the Ministry of Science and Education of the Russian Federation (Grant 1.3464.2017/4.6) and the second author was supported by the Russian Foundation for Basic Research (Grant 16-01-00197).
Citation:
A. G. Baskakov, I. I. Strukova, I. A. Trishina, “Solutions almost periodic at infinity to differential equations with unbounded operator coefficients”, Sibirsk. Mat. Zh., 59:2 (2018), 293–308; Siberian Math. J., 59:2 (2018), 231–242
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\paper Solutions almost periodic at infinity to differential equations with unbounded operator coefficients
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 2
\pages 293--308
\mathnet{http://mi.mathnet.ru/smj2972}
\crossref{https://doi.org/10.17377/smzh.2018.59.205}
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\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 2
\pages 231--242
\crossref{https://doi.org/10.1134/S0037446618020052}
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Linking options:
https://www.mathnet.ru/eng/smj2972
https://www.mathnet.ru/eng/smj/v59/i2/p293
This publication is cited in the following 13 articles:
Wei-Gang Jian, Hui-Sheng Ding, “Tauberian theorems on ℝ⁺ and applications”, Proc. Amer. Math. Soc., 2024
Hui-Sheng Ding, Wei-Gang Jian, Nguyen Van Minh, Gaston M. N'Guérékata, “Kadets type and Loomis type theorems for asymptotically almost periodic functions”, Journal of Differential Equations, 373 (2023), 389
Jian Wei-Gang, Ding Hui-Sheng, “Loomis type 定理 on the half-line and its application”, Sci. Sin.-Math., 53:9 (2023), 1241
I. A. Vysotskaya, “Solutions of Difference Equations Almost Periodic at Infinity”, J Math Sci, 263:5 (2022), 635
I. I. Strukova, “On Some Properties of Functions Almost Periodic at Infinity from Homogeneous Spaces”, J Math Sci, 263:5 (2022), 643
V. E. Strukov, “On Distributions That Are Almost Periodic at Infinity”, J Math Sci, 263:4 (2022), 511
I. A. Vysotskaya, I. I. Strukova, “Issledovanie nekotorykh klassov pochti periodicheskikh na beskonechnosti funktsii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 21:1 (2021), 4–14
A. G. Baskakov, V. E. Strukov, I. I. Strukova, “Almost periodic at infinity functions from homogeneous spaces as solutions to differential equations with unbounded operator coefficients”, Eurasian Math. J., 11:4 (2020), 8–24
A. G. Baskakov, V. E. Strukov, I. I. Strukova, “Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity”, Sb. Math., 210:10 (2019), 1380–1427
V. E. Strukov, “O raspredeleniyakh, pochti periodicheskikh na beskonechnosti”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 170, VINITI RAN, M., 2019, 51–61
I. I. Strukova, “O nekotorykh svoistvakh pochti periodicheskikh na beskonechnosti funktsii iz odnorodnykh prostranstv”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 171, VINITI RAN, M., 2019, 47–56
I. A. Vysotskaya, “Pochti periodicheskie na beskonechnosti resheniya raznostnykh uravnenii”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 171, VINITI RAN, M., 2019, 38–46
A. G. Baskakov, V. E. Strukov, I. I. Strukova, “On the almost periodic at infinity functions from homogeneous spaces”, Probl. anal. Issues Anal., 7(25):2 (2018), 3–19
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