On A Characterization of Compactness and the Abel-Poisson Summability of Fourier Coefficients In Banach Spaces

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FILOMAT, vol.30, no.4, pp.1061-1068, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1604061o
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1061-1068
  • Karadeniz Technical University Affiliated: No


In this paper, for an isometric strongly continuous linear representation denoted by alpha of the topological group of the unit circle in complex Banach space, we study an integral representation for Abel-Poisson mean A(r)(alpha)(x) of the Fourier coefficients family of an element x, and it is proved that this family is Abel-Poisson summable to x. Finally, we give some tests which are related to characterizations of relatively compactness of a subset by means of Abel-Poisson operator A(r)(alpha) and alpha.