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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 23, Issue 3

Issues

Summation of smooth functions of two variables with perturbed Fourier coefficients

Sergey G. Solodky / Kosnazar K. Sharipov
  • Faculty of Mechanics and Mathematics, National Taras Sevchenko University of Kiev, Academician Glushkov Pros. 4-E, 03127, Kiev, Ukraine
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Published Online: 2014-11-09 | DOI: https://doi.org/10.1515/jiip-2013-0076

Abstract

The present paper is devoted to the problem of recovering smooth functions from their Fourier coefficients. We consider the functions of two variables. Herewith this problem is ill-posed. The problem is studied in the case of given smoothness of the functions as well as when a parameter of smoothness is supposed to be unknown.

Keywords: Ill-posed problem; regularization method; hyperbolic cross; balancing principle

MSC: 42C05; 42A24; 65J20

About the article

Received: 2013-12-02

Revised: 2014-02-12

Accepted: 2014-08-15

Published Online: 2014-11-09

Published in Print: 2015-06-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 23, Issue 3, Pages 287–297, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2013-0076.

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[1]
K.K. Sharipov
International Journal of Computer Mathematics, 2016, Volume 93, Number 10, Page 1708

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