Determination of a jump by Fourier and Fourier-Chebyshev series

Author(s):

M. Avdispahic , Z. Sabanac *

Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
ýBy observing the equivalence of assertions on determining the jump of aý ýfunction by its differentiated or integrated Fourier seriesý, ýwe generalize aý ýprevious result of Kvernadzeý, ýHagstrom and Shapiro to the whole class ofý ýfunctions of harmonic bounded variationý. ýThis is achieved without the finiteness assumption oný ýthe number of discontinuitiesý. ýTwo results on determination of jumpý ýdiscontinuities by means of the tails of integrated Fourier-Chebyshev series are also derived.
Keywords:

Fourier series? , ?generalized bounded variation? , ?jump discontinuities?

Language:
English
Published:
Bulletin of Iranian Mathematical Society, Volume:43 Issue: 7, 2017
Pages:
2307 to 2321
https://www.magiran.com/p1850905