Mathematica Pannonica
Volume/Issue:
Volume 27_NS1: Issue 2
On the Negativity of the Walsh–Kaczmarz–Riesz Logarithmic Kernels
Authors:
György Gát Institute of Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400, Hungary

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Gábor Lucskai Institute of Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400, Hungary
Institute of Mathematics and Informatics, University of Pécs, H-7624 Pécs, Ifjúság u. 6

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Pages:
197–203
Online Publication Date:
26 Oct 2021
Publication Date:
18 Nov 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2021.00018
Keywords (English):
Walsh–Kaczmarz; Riesz logarithmic kernel
Open access

The main aim of this paper is to prove that the nonnegativity of the Riesz’s logarithmic kernels with respect to the Walsh– Kaczmarz system fails to hold.

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    Schipp, F., Wade, W. R., Simon, P., and Pál, J. Walsh series: an introduction to dyadic harmonic analysis. Adam Hilger, Bristol and New York, 1990.

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    Zygmund, A. Trigonometric Series.. University Press, Cambridge, 1959 (English).

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    Gat, G. On (C,1)summability of integrable functions with respect to the Walsh–Kaczmarz system. Studia Math 130, 2 (1998), 135–148.

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    Gat, G., and Goginava, U. Uniform and L-convergence of logarithmic means of Walsh-Fourier series, Acta Mathematica Sinica 22, 2 (2006), 497–506.

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    Hardy, G. H. The summability of a Fourier series by logarithmic means. The Quarterly Journal of Mathematics 1, (1931), 107–112.

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    Skvorcov, V. A. On Fourier series with respect to the Walsh–Kaczmarz system. Analysis Math. 7 (1981), 141–150.

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    Skvorcov, V. A. Convergence in L1 of Fourier series with respect to the Walsh–Kaczmarz system. Vestnik Mosk. Univ. Ser. Mat. Meh. 6 (1981), 3–6.

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    Young, R. M. Euler’s Constant. The Mathematical Gazette 75, 472 (Jun. 1991), 187–190.

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • Attila BÉRCZES (University of Debrecen)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • György DÓSA (University of Pannonia, Veszprém)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Gábor NYUL (University of Debrecen)
  • Margit PAP (University of Pécs)
  • István PINK (University of Debrecen)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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