Document Zbl 0322.43014

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

J. Funct. Anal. 22, 73-105 (1976).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of 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.)

Cite Review PDF

Full Text: DOI

Digital Library of Mathematical Functions:

§35.5(i) Definitions ‣ §35.5 Bessel Functions of Matrix Argument ‣ Properties ‣ Chapter 35 Functions of Matrix Argument

References:

[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, (Symmetric Spaces (1972), Marcel Dekker: Marcel Dekker New York), 119-139 · Zbl 0268.43010
[3]	K. I. Gross and R. A. Kunzein; K. I. Gross and R. A. Kunzein
[4]	Gross, K. I.; Kunze, R. A., Generalized Bessel transforms and unitary representation, (Harmonic Analysis on Homogeneous Spaces. Harmonic Analysis on Homogeneous Spaces, Amer. Math. Soc. Symposium XXVI (1973)), 347-350 · Zbl 0289.22014
[5]	K. I. Gross and R. A. Kunze; K. I. Gross and R. A. Kunze · Zbl 0567.22007
[6]	K. I. Gross and R. A. KunzeIIJ. Functional Analysis; K. I. Gross and R. A. KunzeIIJ. Functional Analysis · 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: 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, (Proceedings of the Conference on Functional Analysis at Irvine. Proceedings of the Conference on Functional Analysis at Irvine, California (1966), Thompson Book Company) · Zbl 0226.43011
[11]	Naimark, M. A., Normed Algebras (1972), Wolters-Noordhoff: Wolters-Noordhoff Groningen · Zbl 0073.08902
[12]	H. Rossi and M. VergneActa Math.; H. Rossi and M. VergneActa Math. · 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 Univ. Press Princeton, N.J · Zbl 0232.42007
[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: 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.