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ANALYTIC CONTINUATION OF THE IRREDUCIBLE UNITARY
n Irreducible unitary representations of the universal covering group
Analytic continuation of the principal series
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Analytic Continuation of the Irreducible Unitary Representations of the ...
Paul J. Sally
Limited preview - 1967
absolutely convergent analytic continuation analytic operator valued Bargmann basis for H Bessel function bounded operator canonical basis Chapter complementary series complex number compute consider the operator construct continuous representation COROLLARY corresponding cos(h cosh t/2 decomposition defines a continuous definition dense subspace f and g fixed h following Lemma formula Fubini's theorem function defined function f G on H group G Hilbert space holomorphic holomorphic functions implies inner product integral irreducible unitary representations isometric isomorphic Lemma Math matrix elements Mellin transform negative discrete series normalized discrete series normalized principal series operator valued function orthonormal basis positive discrete series proof of Theorem properties prove Remarks representation a—>R a,h representation operators representation spaces representations of G respect s£iR series of representations sGiR space H subgroups of G tanh t/2 tion uniformly bounded representations unitarily equivalent unitary map unitary operator universal covering group well-defined