On the convergence of the Abel–Poisson means of multiple Fourier series

Sezer S., ERYİĞİT M., BAYRAKÇI DOĞAN S.

Turkish Journal of Mathematics, vol.46, no.4, pp.1302-1309, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2112-58
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1302-1309
  • Keywords: Abel–poisson means, Multiple fourier series, Poisson summation formula
  • Akdeniz University Affiliated: Yes

Abstract

© This work is licensed under a Creative Commons Attribution 4.0 International License.Let Aε(x, f) be the Abel–Poisson means of an integrable function f(x) on n–dimensional torus Tn, (Formula Presented) in the Euclidean n–space. The famous Bochner’s theorem asserts that for any function (Formula Presented) the Abel–Poisson means Aε(x, f) are pointwise converge to f(x) a.e., that is, (Formula Presented), a.e. x ∈ Tn. In this paper we investigate the rate of convergence of Abel–Poisson means at the so-called μ–smoothness point of f.