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Bessel functions and representation theory. I. (English) Zbl 0322.43014


MSC:

43A80 Analysis on other specific Lie groups
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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[2] Gross, K.I; Kunze, R.A, Fourier decompositions of certain representations, (), 119-139 · Zbl 0268.43010
[3] {\scK. I. Gross and R. A. Kunze}, Fourier-Bessel transforms and holomorphic discrete series, in “Conference in Harmonic Analysis,” pp. 79-122, Springer Lecture Notes #266.
[4] Gross, K.I; Kunze, R.A, Generalized Bessel transforms and unitary representation, (), 347-350
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[6] {\scK. I. Gross and R. A. Kunze}, Bessel functions and representation theory II, J. Functional Analysis, to appear. · Zbl 0322.43014
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[13] Segal, I.E, Transforms for operators and symplectic automorphisms over a locally compact abelian group, Math. scand., 13, 31-43, (1963) · Zbl 0208.39002
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