Generalization of the Newman–Shapiro isometry theorem and Toeplitz operators. II
Volume 150 / 2002
Studia Mathematica 150 (2002), 175-188
MSC: Primary 47B35; Secondary 46E20, 46E40.
DOI: 10.4064/sm150-2-6
Abstract
The Newman–Shapiro Isometry Theorem is proved in the case of Segal–Bargmann spaces of entire vector-valued functions (i.e. summable with respect to the Gaussian measure on ${\mathbb C}^n$). The theorem is applied to find the adjoint of an unbounded Toeplitz operator $T_{\varphi }$ with $\varphi $ being an operator-valued exponential polynomial.
