The Finite Rank Theorem for Toeplitz Operators on the Fock Space

We consider Toeplitz operators on the Fock space, under rather general conditions imposed on the symbols. We prove that if a Toeplitz operator has finite rank, then the operator and its symbol are zero. Our argument is somewhat different from the ones used previously for finite rank theorem, and it enables us to get rid of the compact support condition and even allows for a certain growth of the symbol