Local property of absolute weighted mean summability of Fourier series

Rhoades B., SAVAŞ E.

Applied Mathematics and Computation, vol.153, no.2, pp.445-452, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 153 Issue: 2
  • Publication Date: 2004
  • Doi Number: 10.1016/s0096-3003(03)00644-1
  • Journal Name: Applied Mathematics and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.445-452
  • Keywords: Absolute summability, Local property, Summability factors, Weighted mean
  • Uşak University Affiliated: Yes

Abstract

A theorem on a local property of absolute weighted mean summability of factored Fourier series and a summability factor theorem for Fourier series was obtained. It was assumed that the constant term in the Fourier series representation for f is zero. It was observed that the convergence of the Fourier series of f at t=x is a local property of f. It was shown that the summability of the Fourier series at t=x by any regular summability method is also a local property of f.