APPROXIMATION BY GENERALIZED FABER SERIES IN BERS SPACES ON QUASIDISKS

M. Sun

IJPAM: Volume 113, No. 2 (2017)

Title

APPROXIMATION BY GENERALIZED FABER SERIES
IN BERS SPACES ON QUASIDISKS

Authors

Mingfeng Sun
Department of Mathematics
Shaoxing University
Shaoxing, Zhejiang 312000, P.R. CHINA

Abstract

In this paper, by the conformal natural reflection introduced by Earle and Nag ,we establish an integral representation for Bers space

where

is a quasidisk, and then we define generalized Faber series of functions in

. We find a subspace

such that each $\varphi\in B_1(D)$ converges uniformly on compact subsets of

. Also, if a series $\sum_{m=3}^{\infty}a_mF_m^{'''}(z)$ is convergent to $\varphi\in B_1(D)$ in the norm $\Vert\Vert _D$ , we show that the

are the generalized Faber coefficients $a_m(\varphi)$ of $\varphi$ .

History

Received: October 26, 2016
Revised: December 12, 2016
Published: March 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 30C62,30C10
Key Words and Phrases: Faber series, Bers space, quasidisk,reproducing formula, conformally natural reflection

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How to Cite?

DOI: 10.12732/ijpam.v113i2.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 2
Pages: 241 - 250

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