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Approximation of entire functions over Carathéodory domains

Published online by Cambridge University Press:  17 April 2009

G.P. Kapoor  and
A. Nautiyal
G.P. Kapoor
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India.
A. Nautiyal
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India.
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Abstract

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Let D be a domain bounded by a Jordan curve. For 1 ≤ p ≤ ∞, let Lp(D) be the class of all functions f holomorphic in D such that where A is the area of D. For f ∈Lp(D), set

πn consists of all polynomials of degree at most n. Recently, Andre Giroux (J. Approx. Theory 28 (1980), 45–53) has obtained necessary and sufficient conditions, in terms of the rate of decrease of the approximation error , such that has an analytic continuation as an entire function having finite order and finite type. In the present paper we have considered the approximation error (*) on a Carathéodory domain and have extended the results of Giroux for the case 1 ≤ p < 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 2 , April 1982 , pp. 221 - 229
Copyright
Copyright © Australian Mathematical Society 1982

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