Fourier expansions of entire functions

Abstract

Let E denote a compact Jordan region in the complex plane with positive transfinite diameter and H(E) the Hubert space of entire functions. This paper is deals with relations connecting the (p, q)-growth of an entire function f $epsilon$ H(E) with its Fourier coefficients with respect to an orthonormal sequence of polynomials in H(E). The (p, q)-order and generalized (p, q)-type have been characterized in terms of Fourier coefficients for f $epsilon$ H(E).