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


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.)
Full Text: DOI


[1] Gelbart, S, A theory of Stiefel harmonics, Trans. amer. math. soc., 192, 29-50, (1974) · Zbl 0292.22016
[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
[5] {\scK. I. Gross and R. A. Kunze}, Finite dimensional induction and invariants for groups of forms, in preparation. · Zbl 0567.22007
[6] {\scK. I. Gross and R. A. Kunze}, Bessel functions and representation theory II, J. Functional Analysis, to appear. · Zbl 0322.43014
[7] Helgason, S, Invariants and fundamental functions, Acta. math., 109, 241-258, (1963) · Zbl 0112.26303
[8] Helgason, S, Differential geometry and symmetric spaces, (1962), Academic Press New York · Zbl 0122.39901
[9] Herz, C, Bessel functions of a matrix argument, Ann. of math., 61, 474-523, (1955) · Zbl 0066.32002
[10] Kunze, R.A, Positive definite operator-valued kernels and unitary representations, () · Zbl 0226.43011
[11] Naimark, M.A, Normed algebras, (1972), Wolters-Noordhoff Groningen · Zbl 0073.08902
[12] {\scH. Rossi and M. Vergne}, Analytic continuation of the holomorphic discrete series of a semi-simple Lie group, Acta Math. to appear. · Zbl 0356.32020
[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
[14] Shale, D, Linear symmetries of free boson fields, Trans. amer. math. soc., 103, 149-167, (1962) · Zbl 0171.46901
[15] Stein, E.M; Weiss, G, Introduction to harmonic analysis on Euclidean space, (1971), Princeton Univ. Press Princeton, N.J
[16] Weil, A, Sur certains groupes d’opérateurs unitaires, Acta math., 111, 143-211, (1964) · Zbl 0203.03305
[17] Weil, A, Basic number theory, (1967), Springer New York · Zbl 0176.33601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.