Fourier expansions of entire functions

Abstract

Let E denote a compact lordan region in the complcx plane with positive transfinite diameter and H(E) the Hilbert space of entire functions. This paper is deals with relations connecting the (p, q)-growth of an entire function f e 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 e H(E).