Zero sums of dual Toeplitz products on the orthogonal complements of the polyanalytic Fock space

Abstract

We consider dual Toeplitz operators on the orthogonal complement of the polyanalytic Fock space of the complex plane. We characterize the zero sum of products of two dual Toeplitz operators with harmonic symbols. Our results extend several known results on the analytic Fock space to every polyanalytic Fock spaces.