Riesz Basis in de Branges Spaces of Entire Functions

Abstract

In this paper we consider the problem of Riesz basis in de Branges spaces of entire functions H(E) with the condition that ϕ 0 (x) ≥ α > 0, where ϕ is the corresponding phase function. We are concerned with the sets of real numbers {λn} such that the normalized reproducing kernels k(λn, .)/kk(λn, .)k satisfies the restricted isometry property, which in turn constitute a Riesz basis in H(E). Then we give a criterion on stability of reproducing kernels corresponding to real points which form a Riesz basis in H(E) with respect to small perturbations, which generalize some well-known Riesz basis perturbation results in the Paley-Wiener space.