Abstract
In this paper, a general theory of operator-valued Bessel functions on mixed Schrödinger-Fock spaces and Siegel domains of type II is presented. In general, Bessel functions J λ are associated to the partial Fourier transform on a mixed Schrödinger-Fock space. J λ can be realized as a reduced Bessel function K π , which is a generalized inverse Laplace transform on a Siegel domain of type II. The application of this theory to representation theory will be studied in the next paper.
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