Vol. 36, No. 2, 1971

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On weighted polynomial approximation of entire functions

Bert Alan Taylor

Vol. 36 (1971), No. 2, 523–539
Abstract

An existence theorem for the operator is used here to prove some results on weighted approximation of entire functions. Theorem 2 shows that if ϕ is a convex function on Cn = R2n such that the Hilbert space of all entire functions f with |f|2edλ < +( Lebesgue measure) contains the polynomials, then the polynomials are dense in this Hilbert space. Two approximation theorems are also given which are related to the theory of quasi-analytic functions.

Mathematical Subject Classification
Primary: 46.30
Secondary: 32.00
Milestones
Received: 23 April 1969
Published: 1 February 1971
Authors
Bert Alan Taylor