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


Cavus A.

JOURNAL OF APPROXIMATION THEORY, cilt.87, ss.25-35, 1996 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 87 Konu: 1
  • Basım Tarihi: 1996
  • Doi Numarası: 10.1006/jath.1996.0090
  • Dergi Adı: JOURNAL OF APPROXIMATION THEORY
  • Sayfa Sayıları: ss.25-35

Özet

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.