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Integral operators with kernels that are discontinuous on broken lines. (English. Russian original) Zbl 1203.47025

Sb. Math. 197, No. 11, 1669-1696 (2006); translation from Mat. Sb. 197, No. 11, 115-142 (2006).
Summary: 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.

MSC:

47G10 Integral operators
42A24 Summability and absolute summability of Fourier and trigonometric series
45P05 Integral operators
47A10 Spectrum, resolvent
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
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