Some Applications of Spaces of Entire Functions

Abstract

A Hilbert space, whose elements are entire functions, is of particular interest if it has these properties:(H1) Whenever F(z) is in the space and has a non-real zero w, the function is in the space and has the same norm as F(z).(H2) For each non-real number w, the linear functional defined on the space by F(z) —> F(w) is continuous.(H3) Whenever F(z) is in the space, is in the space and has the same norm as F(z). If E(z) is an entire function satisfying