Abstract:
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.
Citation:
A. G. Baskakov, N. S. Kaluzhina, D. M. Polyakov, “Slowly varying on infinity semigroups of operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 7, 3–14; Russian Math. (Iz. VUZ), 58:7 (2014), 1–10
This publication is cited in the following 15 articles:
Wei-Gang Jian, Hui-Sheng Ding, “Tauberian theorems on ℝ⁺ and applications”, Proc. Amer. Math. Soc., 2024
Li Chen-Yu, “Asymptotic Stability of Riemann–Liouville Fractional Resolvent Families”, Results Math, 78:6 (2023)
S. I. Piskarev, A. V. Ovchinnikov, “Attraktory, zatenenie i approksimatsiya abstraktnykh polulineinykh differentsialnykh uravnenii”, Funktsionalnyi analiz, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 189, VINITI RAN, M., 2021, 3–130
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
V. E. Strukov, I. I. Strukova, “Garmonicheskii analiz medlenno menyayuschikhsya na beskonechnosti polugrupp operatorov”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 19:2 (2019), 152–163
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, I. I. Strukova, I. A. Trishina, “Solutions almost periodic at infinity to differential equations with unbounded operator coefficients”, Siberian Math. J., 59:2 (2018), 231–242
A. A. Ryzhkova, “Garmonicheskii analiz periodicheskikh na beskonechnosti posledovatelnostei”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 22–32
A. G. Baskakov, T. K. Katsaran, T. I. Smagina, “Linear differential second-order equations in Banach space and splitting of operators”, Russian Math. (Iz. VUZ), 61:10 (2017), 32–43
I. A. Trishina, “Pochti periodicheskie na beskonechnosti funktsii otnositelno podprostranstva integralno ubyvayuschikh na beskonechnosti funktsii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 17:4 (2017), 402–418
M. S. Bichegkuev, “Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients”, Math. Notes, 99:1 (2016), 24–36
I. I. Strukova, “On Wiener's Theorem for functions periodic at infinity”, Siberian Math. J., 57:1 (2016), 145–154
A. G. Baskakov, “Harmonic and Spectral Analysis of Power Bounded Operators and Bounded Semigroups of Operators on Banach Spaces”, Math. Notes, 97:2 (2015), 164–178
A. A. Ryzhkova, I. A. Trishina, “O pochti periodicheskikh na beskonechnosti resheniyakh raznostnykh uravnenii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 15:1 (2015), 45–49
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