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 Mat. Sb., 2019, Volume 210, Number 10, Pages 37–90 (Mi msb9147)

Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity

A. G. Baskakov, V. E. Strukov, I. I. Strukova

Voronezh State University, Voronezh, Russia

Abstract: Vector-valued functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity are investigated. The concept of the Fourier series of a function (distribution), periodic or almost periodic at infinity, with coefficients that are functions (distributions) slowly varying at infinity, is introduced. The properties of the Fourier series are investigated and an analogue of Wiener's theorem on absolutely convergent Fourier series is obtained for functions periodic at infinity. Special attention is given to criteria ensuring that solutions of differential or difference equations are periodic or almost periodic at infinity. The central results involve theorems on the asymptotic behaviour of a bounded operator semigroup whose generator has no limit points on the imaginary axis. In addition, the concept of an asymptotically finite-dimensional operator semigroup is introduced and a theorem on the structure of such a semigroup is proved.
Bibliography: 39 titles.

Keywords: function periodic at infinity, function almost periodic at infinity, homogeneous space, operator semigroup, differential equation.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 1.3464.2017/4.6 Russian Foundation for Basic Research 18-31-00097-ìîë_à19-01-00732-a16-01-00197-à The research of A. G. Baskakov was carried out in the framework of a state assignment from the Ministry of Education and Science of the Russian Federation (project no. 1.3464.2017/4.6). The research of V. E. Strukov was carried out with the support of the Russian Foundation for Basic Research (grant no. 18-31-00097-ìîë_à). The research of I. I. Strukova was carried out with the support of the Russian Foundation for Basic Research (grant nos. 19-01-00732-a and 16-01-00197-a).

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DOI: https://doi.org/10.4213/sm9147

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English version:
Sbornik: Mathematics, 2019, 210:10, 1380–1427

Bibliographic databases:

UDC: 517.98
MSC: 42A75, 46E40, 46F05

Citation: 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”, Mat. Sb., 210:10 (2019), 37–90; Sb. Math., 210:10 (2019), 1380–1427

Citation in format AMSBIB
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