Operator-valued Bessel functions, holomorphic discrete series, and harmonic representations of U(p, q)

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This paper presents representation-theoretic applications of the theory of operator-valued Bessel functions, which was developed in the first paper of this series. Using the reduced Bessel function K π we study the harmonic representation and holomorphic discrete series for the group U(p,q) of biholomorphic automorphisms of the Siegel domains of type II.