Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Koroleva O. A. An Analogue of the Jordan–Dirichlet Theorem for the Integral Operator with Kernel Having Jumps on Broken Lines. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 14-23. DOI: 10.18500/1816-9791-2013-13-4-14-23

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.12.2013
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Russian
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517.984

An Analogue of the Jordan–Dirichlet Theorem for the Integral Operator with Kernel Having Jumps on Broken Lines

Autors: 
Koroleva Olga Arturovna, Saratov State University
Abstract: 

In this paper the sufficient conditions (conditions such as Jordan–Dirichlet) expansion function f(x) in a uniformly convergent series of eigenfunctions and associated functions of the integral operator whose kernel is suffering jumps on the sides of the square, inscribed in the unit square. As is known, this expansion requires to f(x) is continuous and belong to the closure of the integral values operator. It turns out that if f(x) also is a function of bounded variation, these conditions are also sufficient.

References: 
  1. Khromov А. P. Integral operators with kernels that are discontinuous on broken lines. Sbornik:Mathematics, 2006, vol. 197, no. 11, pp. 1669–1696. DOI:10.4213/sm1534.
  2. Koroleva O A., Khromov А. P. Integral operator with a kernel that has jumps on broken lines. Izv. Sarat. Univ. N.S. Ser. Math. Mech. Inform., 2012, vol. 12, iss. 2, pp. 6–13 (in Russian).
  3. Kornev V. V., Khromov А. P. Uniform convergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals. Sbornik: Mathematics, 2001, vol. 192, no. 10, pp. 1451—1469. DOI:10.4213/sm601.
  4. Koroleva O A. On Convergence of Riesz Means of the Expansions in Eigen and Associated Functions Integral Operator with Kernel Having Jumps on Broken Lines. Izv. Sarat. Univ. N.S. Ser. Math. Mech. Inform., 2013,  vol. 1, iss. 2, pp. 63–67 (in Russian).
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