Unbounded Toeplitz Operators in the Segal-Bargmann Space, II

The paper mostly deals with the questions of closedness and essential selfadjointness of Toeplitz operators in the Segal-Bargmann space. General criteria for their closedness are formulated. Examples of unclosed Toeplitz operators are given. Explicit formulas for their adjoints are shown for various classes of symbols. The problem of whether polynomials and exponents form cores for Toeplitz operators is investigated. The results presented here improve and extend the ones from an earlier paper.