Determination of jumps in terms of Abel–Poisson means

F. Móricz

doi:10.1023/a:1022830026744

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Acta Mathematica Hungarica

Volume/Issue:: Volume 98: Issue 3

Determination of jumps in terms of Abel–Poisson means

Author:

F. Móricz

F. Móricz University of Szeged Aradi Vértanúk tere 1 Bolyai Institute 720 Szeged Hungary 720 Szeged Hungary

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Pages:: 259–262

Online Publication Date:: 03 Nov 2004

Publication Date:: 01 Feb 2002

Article Category:: Research Article

DOI:: https://doi.org/10.1023/a:1022830026744

Keywords:: conjugate series; jump of a function; Fourier series; atom; Abel–Poisson mean; finite Borel measure

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Abstract

A theorem of Ferenc Lukcs determines the jumps of a periodic, Lebesgue integrable function f at each point of discontinuity of first kind in terms of the partial sums of the conjugate series to the Fourier series of f. The aim of this note is to prove an analogous theorem in terms of the Abel-Poisson means.

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Acta Mathematica Hungarica

Print ISSN:: 0236-5294

Online ISSN:: 1588-2632

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Acta Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1950
Volumes per Year	3
Issues per Year	6
Founder	Magyar Tudományos Akadémia
Founder's Address	H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0236-5294 (Print)
ISSN	1588-2632 (Online)