Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Strukova I. I. Harmonic Analysis of Periodic at Infinity Functions from Stepanov Spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, vol. 17, iss. 2, pp. 172-182. DOI: 10.18500/1816-9791-2017-17-2-172-182

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
22.05.2017
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Russian
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UDC: 
517.9

Harmonic Analysis of Periodic at Infinity Functions from Stepanov Spaces

Autors: 
Strukova Irina Igorevna, Voronezh State University, Russia
Abstract: 

We consider Stepanov spaces of functions defined on 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 Cesaro summability. Basic results are derived with the use of isometric representations theory.

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