Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Nazarova E. V., Khalova V. A. Equiconvergence Theorem for Integral Operator with Involution. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, vol. 17, iss. 3, pp. 313-330. DOI: 10.18500/1816-9791-2017-17-3-313-330, EDN: ZEGHVB

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.08.2017
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Russian
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UDC: 
517.984
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ZEGHVB

Equiconvergence Theorem for Integral Operator with Involution

Autors: 
Nazarova Ekaterina V., Educational institution of the Central Bank of the Russian Federation
Khalova Victoria Anatol'evna, Saratov State University
Abstract: 

In the paper, the integral operator with kernel having discontinuities of the first kind at the lines t = x and t = 1 − x is studied. The equiconvergence of Fourier expansions for arbitrary integrable function f(x) in eigenfunctions and associated functions of the considered operator and expansions of linear combination of functions f(x) and f(1 − x) in trigonometric system is proved. The equiconvergence is studied using the method based on integration of the resolvent using spectral value. Methods, developed by A. P. Khromov in the study of spectral theory of integral operators are widely used. Recently, these methods are of use in studies of boundary value problems of mathematical physics using Fourier method with minimal smoothness conditions for the initial data.

References: 
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Received: 
22.04.2017
Accepted: 
28.07.2017
Published: 
01.09.2017
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