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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2006 Volume 197, Number 11, Pages 115–142 (Mi sm1534)

This article is cited in 26 papers

Integral operators with kernels that are discontinuous on broken lines

A. P. Khromov

Saratov State University named after N. G. Chernyshevsky

Abstract: In this paper we study the equiconvergence of expansions in trigonometric Fourier series and in eigenfunctions and associated functions of an integral operator whose kernel has discontinuities of the first kind on broken lines formed from the sides and diagonals of the squares obtained by dividing the unit square into $n^2$ equal squares.
Bibliography: 11 titles.

UDC: 517.984

MSC: Primary 47G10; Secondary 42A24, 45P05, 47A10, 47A70

Received: 20.02.2006

DOI: 10.4213/sm1534


 English version:
Sbornik: Mathematics, 2006, 197:11, 1669–1696

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© Steklov Math. Inst. of RAS, 2025