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 Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.: Year: Volume: Issue: Page: Find

 Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2017, Volume 17, Issue 2, Pages 172–182 (Mi isu714)

Scientific Part
Mathematics

Harmonic analysis of periodic at infinity functions from Stepanov spaces

I. I. Strukova

Voronezh State University, 1, Universitetskaya pl., Voronezh, Russia, 394036

Abstract: We consider Stepanov spaces of functions defined on $\mathbb{R}$ with their values in a complex Banach space. We introduce the notions of slowly varying and periodic at infinity functions from Stepanov space. The main results of the article are concerned with harmonic analysis of periodic at infinity functions from Stepanov space. For this class of functions we introduce the notion of a generalized Fourier series; the Fourier coefficients in this case may not be constants, they are functions that are slowly varying at infinity. We prove analogs of the classical results on Ćesaro summability. Basic results are derived with the use of isometric representations theory.

Key words: Banach space, $L^1(\mathbb{R})$-module, Stepanov space, slowly varying at infinity function, periodic at infinity function, Fourier series.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00197_à This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00197 performed in Voronezh State University).

DOI: https://doi.org/10.18500/1816-9791-2017-17-2-172-182

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Document Type: Article
UDC: 517.9

Citation: I. I. Strukova, “Harmonic analysis of periodic at infinity functions from Stepanov spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 17:2 (2017), 172–182

Citation in format AMSBIB
\Bibitem{Str17} \by I.~I.~Strukova \paper Harmonic analysis of periodic at infinity functions from Stepanov spaces \jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform. \yr 2017 \vol 17 \issue 2 \pages 172--182 \mathnet{http://mi.mathnet.ru/isu714} \crossref{https://doi.org/10.18500/1816-9791-2017-17-2-172-182} \elib{http://elibrary.ru/item.asp?id=29924696}