On Hilbert Spaces of Entire Functions with Unconditional Bases of Reproducing Kernels

Abstract

We consider an entire function under certain conditions on the distribution of its zeros. We construct a Hilbert space of entire functions which possess unconditional basis of reproducing kernels at zeros of this function. It is proved that some known Hilbert spaces of entire functions with unconditional bases of reproducing kernels are isomorphic (as normalized spaces) to the corresponding spaces constructed by the entire functions generating the bases.