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Mathematical Notes

, Volume 105, Issue 3–4, pp 543–549 | Cite as

A Sobolev Orthogonal System of Functions Generated by a Walsh System

  • M. G. Magomed-KasumovEmail author
Article
  • 27 Downloads

Abstract

Properties of functions from the Sobolev orthogonal system \(\mathfrak{W}_{r}\) generated by the Walsh system are studied. In particular, recurrence relations for functions from \(\mathfrak{W}_{1}\) are obtained. The uniform convergence of Fourier series in the system \(\mathfrak{W}_{r}\) to functions f from the S obolev spaces \(W_{{L^p}}^r\), p ≥ 1, r = 1, 2,… is proved.

Keywords

Sobolev orthogonality Walsh system uniform convergence recurrence relation 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Vladikavkaz Scientific Center of Russian Academy of SciencesVladikavkazRussia
  2. 2.Daghestan Scientific Center of Russian Academy of SciencesMakhachkalaRussia

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