Marcinkiewicz-Zygmund inequalities for polynomials in Fock space

Abstract

We study the relation between Marcinkiewicz-Zygmund families for polynomials in a weighted $$L^2$$ L 2 -space and sampling theorems for entire functions in the Fock space and the dual relation between uniform interpolating families for polynomials and interpolating sequences. As a consequence we obtain a description of signal subspaces spanned by Hermite functions by means of Gabor frames.