Generalization of the Newman--Shapiro isometry theorem and Toeplitz operators. II (Q2773436)

The paper represents a continuation of author's previous paper with the same title [Integral Equations Oper. Theory 34, No. 4, 414-438 (1999; Zbl 0939.46018)]. It is devoted to the so called Newman-Shapiro isometry theorem which proved to be useful in applications to analytic Toeplitz operators. The generalized Newmann-Shapiro isometry theorem is proved in the case of Segal-Bargmann spaces of entire vector-valued functions integrable with respect to the Gaussian measure on \(\mathbb{C}^n\). The author also gives an application of this theorem to a problem of construction of the adjoint to an unbounded Toeplitz operator \(T_\varphi\) in the case where \(\varphi\) is an operator-valued exponential polynomial.