Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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Strukova I. I. About harmonic analysis of periodic at infinity functions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 1, pp. 28-38. DOI: 10.18500/1816-9791-2014-14-1-28-38, EDN: SCSSRB

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.03.2014
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.9
DOI: 
10.18500/1816-9791-2014-14-1-28-38
EDN: 
SCSSRB

About harmonic analysis of periodic at infinity functions

Autors: 
Strukova Irina Igorevna, Voronezh State University
Abstract: 

We consider slowly varying and periodic at infinity multivariable functions in Banach space. We introduce the notion of Fourier series of periodic at infinity function, study the properties of Fourier series and their convergence. Basic results are derived with the use of isometric representations theory. 

Key words: 
Banach space
Banach algebra
slowly varying at infinity functions
periodic at infinity functions
Fourier series
modulus of continuity
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Received: 
03.08.2013
Accepted: 
17.01.2014
Published: 
28.02.2014
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