This is a preview of subscription content, log in via an institution to check access.
References
Aronszajn, N.,Theory of reproducing kernels. Transactions of the Amer. Math. Soc.68(1950), 337–404.
Berg, C., Christensen, J. P. R., and P. Ressel. “Harmonic analysis on semigroups”, Graduate Texts in Math., Springer, 1984.
Bruhat, F.,Distributions sur un groupe localement compact, Bull. Soc. Math. France89(1961), 43–75.
Dijk, G. van,On generalized Gelfand Pairs, Proc. of the Jap. Acad., Ser. A,60:1(1984), 30–34.
——,On a class of generalized Gelfand Paris, Mathemtische Zeitschrift193(1986), 581–593.
Dixmier, J., “LesC*-algèbres et leurs représentations”, Gauthier-Villars, Paris, 1964.
Faraut, J.,Distributions sphériques sur les espaces hyperboliques, J. math. pures et appl.5(1979), 369–444.
Gelfand, I. M.,Spherical functions in Symmetric Riemann spaces, Dokl. Akad. Nauk USSR70(1950), 5–8. Amer. Math. Soc. Trans.37(1964), 39–44.
Hilgert, J., and K.-H. Neeb, “Lie semigroups and their Applications”, Lecture Notes in Math.1552, Springer, 1993.
--,Spherical functions on Ol’shanskiį space. Journal of Funct. Anal., to appear.
--,Positive definite spherical functions on Ol’shanskiį spaces, submitted.
Hilgert, J., Ólafsson, G., “Causal Symmetric Spaces, Geometry and Harmonic Analysis”, Acad. Press, 1996.
Hilgert, J., Olafsson, G., and B. Ørsted,Hardy Spaces on Affine Symmetric Spaces, J. reine angew. Math.415(1991), 189–218.
Krötz, B., K.-H. Neeb, and G. Ólafsson,Spherical representations for Mixed Symmetric Spaces, in preparation.
Loos, O., “Symmetric Spaces I: General Theory”, Benjamin, New York, Amsterdam, 1969.
Maurin, K., and L. Maurin,Universelle umhüllende Algebra einer lokalkompakten Gruppe und ihre selbstadjungierten Darstellungen. Anwendungen, Studia Math.24(1964), 227–243.
Maurin, K., “General eigenfunction expansions and unitary representations of topological groups”, Polish Science Publ., Warsaw, 1968.
Neeb, K. — H.,Holomorphic representations of Ol’shanskiį semigroups, in “Semigroups in Algebra, Geometry and Analysis”, K. H. Hofmann et al., eds., de Gruyter, 1995.
--,Semigroup actions on reproducing kernel spaces, submitted.
--,On the complex and convex geometry of Ol’shanskiį semigroups, Preprint10, Institut Mittag-Leffler, 1995–96.
--,On weighted Hardy spaces, in preparation.
--, “Holomorphy and Convexity in Lie Theory”, book in preparation.
Powers, R. T.,Self-adjoint algebras of unbounded operators, Comm. Math. Phys.21(1971), 85–124.
——,Selfadjoint algebras of unbounded operators, II, Transactions of the Amer. Math. Soc.187:1(1974), 261–293.
Schwartz, L.,Sous-espaces hilbertiens et noyaux associés; applications aux représentations des groupes de Lie, Deuxième colloque CBRM sur l’analyse fonctionelle, Liège, 1964.
——,Sous-espaces hilbertiens d’espaces vectoriels topologiques et noyaux associés (noyaux reproduisants), J. Analyse Math.13 (1964), 115–256.
Thomas, E. G. F.,Integral representations of invariant reproducing kernels, Proceedings of the bicentennial congress, Amsterdam, 1978.
——,The Theorem of Bochner-Schwartz-Godement for Generalized Gelfand Pairs, Proc. of the 3rd Paderborn conference on Functional Analysis, Functional Analysis: Surveys and Recent results III, Elsevier Science Publisher, North Holland, 1984, 291–304.
——,Integral representations in conuclear cones, Journal of Convex Analysis1:2(1994), 225–258.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Neeb, KH. On some classes of multiplicity free representations. Manuscripta Math 92, 389–407 (1997). https://doi.org/10.1007/BF02678201
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02678201