Unbounded Toeplitz operators in the Segal-Bargmann space. II (Q1891772)

The authors study the question of closedness and essential selfadjointness of Toeplitz operators in the Segal-Bargmann space. They formulate general criteria for their closedness and give examples of unclosed Toeplitz operators. 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 part I [the first author, Stud. Math. 99, No. 2, 87-99 (1991; Zbl 0766.47004)].