Determination of a jump by Fourier and Fourier-Chebyshev series

Document Type: Research Paper

Authors

University of Sarajevo‎, ‎Deaprtment of Mathematics‎, ‎Zmaja od Bosne 33-35‎, ‎71 000 Sarajevo‎, ‎Bosnia and Herzegovina.

Abstract

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of jump‎ ‎discontinuities by means of the tails of integrated Fourier-Chebyshev series are also derived.

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Main Subjects


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Volume 43, Issue 7
November and December 2017
Pages 2307-2321
  • Receive Date: 30 September 2016
  • Revise Date: 13 March 2017
  • Accept Date: 13 March 2017