The Young type theorem in weighted Fock spaces

Abstract

We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by Young on reproducing kernels in the Paley--Wiener space and a recent result of Belov for the classical Bargmann--Segal--Fock space.