Abstract
We give a generalization of the Newman-Shapiro Isometry Theorem to the case of Hilbert space-valued entire functions, which are square-summable with respect to the Gaussian measure μ on ℂ n , together with some applications in the theory of Toeplitz operators with operator-valued symbols. The study of various properties (such as density of domains, cores, closedness and boundedness from below) of these operators in illustrated with many relevant examples.
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