Abstract:
The results of the paper are obtained for functions from homogeneous spaces of functions defined on a locally compact Abelian group. The notion of the Beurling spectrum, or essential spectrum, of functions is introduced. If a continuous unitary character is an essential point of the spectrum of a function, then it is the c-limit of a linear combination of shifts of the function in question. The notion of a slowly varying function at infinity is introduced, and the properties of such functions are considered. For a parabolic equation with initial function from a homogeneous space, it is proved that the weak solution as a function of the first argument is a slowly varying function at infinity.
Citation:
A. G. Baskakov, N. S. Kaluzhina, “Beurlings theorem for functions with essential spectrum from homogeneous spaces and stabilization of solutions of parabolic equations”, Mat. Zametki, 92:5 (2012), 643–661; Math. Notes, 92:5 (2012), 587–605
\Bibitem{BasKal12}
\by A.~G.~Baskakov, N.~S.~Kaluzhina
\paper Beurlings theorem for functions with essential spectrum from homogeneous spaces and stabilization of solutions of parabolic equations
\jour Mat. Zametki
\yr 2012
\vol 92
\issue 5
\pages 643--661
\mathnet{http://mi.mathnet.ru/mzm8963}
\crossref{https://doi.org/10.4213/mzm8963}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3201473}
\zmath{https://zbmath.org/?q=an:1264.43008}
\elib{https://elibrary.ru/item.asp?id=20731622}
\transl
\jour Math. Notes
\yr 2012
\vol 92
\issue 5
\pages 587--605
\crossref{https://doi.org/10.1134/S0001434612110016}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000314263900001}
\elib{https://elibrary.ru/item.asp?id=20484479}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871837032}
Linking options:
https://www.mathnet.ru/eng/mzm8963
https://doi.org/10.4213/mzm8963
https://www.mathnet.ru/eng/mzm/v92/i5/p643
This publication is cited in the following 26 articles:
I. A. Vysotskaya, “Solutions of Difference Equations Almost Periodic at Infinity”, J Math Sci, 263:5 (2022), 635
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, E. E. Dikarev, “Spectral theory of functions in studying partial differential operators”, Ufa Math. J., 11:1 (2019), 3–18
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
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
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. Baskakov. V. Obukhovskii, P. Zecca, “Almost periodic solutions at infinity of differential equations and inclusions”, J. Math. Anal. Appl., 462:1 (2018), 747–763
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. 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
A. G. Baskakov, L. Yu. Kabantsova, I. D. Kostrub, T. I. Smagina, “Linear differential operators and operator matrices of the second order”, Differ. Equ., 53:1 (2017), 8–17
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. I. Strukova, “Garmonicheskii analiz periodicheskikh na beskonechnosti funktsii v odnorodnykh prostranstvakh”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 2(39), 29–38
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
A. G. Baskakov, I. A. Krishtal, “Spectral analysis of abstract parabolic operators in homogeneous function spaces, II”, Mediterr. J. Math., 14:4 (2017), UNSP 181
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, I. A. Krishtal, “Spectral analysis of abstract parabolic operators in homogeneous function spaces”, Mediterr. J. Math., 13:5 (2016), 2443–2462
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
Citation in format AMSBIB
Contact us: