On a Sufficient Condition for the Existence of Unconditional Bases of Reproducing Kernels in Hilbert Spaces of Entire Functions

We consider a reproducing kernel radial Hilbert space of entire functions and prove a sufficient condition for the existence of unconditional bases of reproducing kernels in terms of norms of monomials. Let the system of monomials {lambda(n), n is an element of Z(+)} is complete in a radial Hilbert space of entire functions H, and u(n) = ln||lambda(n)||, u'(+)(n) = u(n + 1) - u(n), n is an element of Z(+). If for some natural number p the condition inf(n)(u'(+)(n + p) - u'(+)(n)) > 0, holds, then H possesses unconditional basis of reproducing kernels.