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

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

Turkish Journal of Mathematics, cilt.46, sa.4, ss.1302-1309, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3906/mat-2112-58
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1302-1309
  • Anahtar Kelimeler: Abel–poisson means, Multiple fourier series, Poisson summation formula
  • Akdeniz Üniversitesi Adresli: Evet

Özet

© 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.