Approximation by generalized Faber series in Bergman spaces on finite regions with a quasiconformal boundary

Cavus A.

JOURNAL OF APPROXIMATION THEORY, vol.87, no.1, pp.25-35, 1996 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 87 Issue: 1
  • Publication Date: 1996
  • Doi Number: 10.1006/jath.1996.0090
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.25-35
  • Karadeniz Technical University Affiliated: No


In this work, for the first time, generalized Faber series for Functions in the Bergman space A(2)(G) on finite regions with a quasiconformal boundary are defined. and their convergence on compact subsets of G and with respect to the norm on A(2)(G) is investigated. Finally, if S-n(f, z) is the nth partial sum of the generalized Faber series of f is an element of A(2)(G), the discrepancy parallel to f-Sn(f, .)parallel to(A2(G)) is evaluated by E(n),(f, G), the best approximation to f by polynomials of degree n. (C) 1996 Academic Press, Inc.