This is a preview of subscription content, log in via an institution to check access.
References
Baily, W. &Borel, A., Compactification of arithmetic quotients of bounded symmetric domains.Ann. of Math., (2) 84 (1966), 442–528.
Bernat, P., et al.,Représentations des groupes de Lie résolubles. Monographies de la Société Mathématique de France, Dunod, Paris, 1972.
Dixmier, J.,Algèbres enveloppantes. Gauthier-Villars, Paris, 1974.
Ehrenpreis, L., Group Representations and hyperbolic differential equations.
Gindikin, S. G., Analysis on homogeneous domains.Russian Math. Surveys, 19 (1964), 1–89.
Gross, K., Restriction to a parabolic subgroup and irreducibility of degenerate principal series of Sp(2;C).Bull. Amer. Math. Soc., 76 (1970) 1281–1285.
Gross, K. & Kunze, R., Generalized Bessel transforms, and unitary representations.Harmonic analysis on hom. spaces; Proceedings of Sumposia in Pure Mathematics, 26, A.M.S., 1973.
Harish-Chandra, Representations of semi-simple Lie groups.IV. Amer. J. Math., 77 (1955) 743–777. V.Amer. J. Math., 78 (1956) 1–41. VI.Amer. J. Math., 78 (1956) 564–628.
Helgason, S.,Differential Geometry and Symmetric Spaces, Academic, New York, 1962.
Knapp, A. &Okamoto, K., Limits of holomorphic discrete series,J. Funct. Anal., 9 (1972) 375–409.
Korányi, A.,Holomorphic and harmonic functions on bounded symmetric domains. Centro Internazionale Matematico Estivo (C.I.M.E.), III Ciclo, Urbino, 1962. Edizioni Cremonese, Roma, 1968.
Korányi, A. &Stein, E., H2-spaces of generalized half planes.Studia Mathematica 44 (1972), 379–388.
Korányi, A. &Wolf, J., Realization of Hermitian symmetric spaces as generalized half planes.Ann. of Math., 81 (1965) 575–596.
Kunze, R., On the irreducibility on certain multiplier representationsBull. Amer. Math. Soc., 68 (1962) 93–94.
Kunze, R., Positive definite operator valued kernels and unitary representations,Prof. Conf. Functional Anal., Irvine, (ed. Gelbaum).
Moore, C. C., Compactification of symmetric spaces II.Amer. J. Math., 86 (1964) 358–378.
Nussbaum, E. A., The Hansdorff-Bernstein-Widder theorem for semigroups in locally compact Abelian groups.Duke Math. J., 22 (1955) 573–582.
Piateckii-Sapiro, I. I.,Geometry of Classical Domains and the Theory of Automorphic Functions, Fizmatgiz, Moscow, 1961; Dunod, Paris, 1966; Gordon and Breach, New York, 1969.
Pukanszky, L., The Plancherel Formula for the Universal Covering group of SL(R;2).Math. Ann. 156 (1964), 96–143.
Rossi H. &Vergne, M. Representations of certain solvable Lie groups on Hilbert spaces of holomorphic functions and the application to the holomorphic discrete series of a semi-simple Lie group,J. Funct. Anal., 13 (4), (1973), 324–389.
To appear.
Rothaus, O., domains of positivity.Abh. Math. Sem, Univ. Hamburg, (24) (1960) 189–235.
Sally, P.,Analytic continuation of the irreducible unitary representation of the universal covering group of SL(2; R). Memoires of the Amer. Math. Soc. 69, Providence, R.I., 1967.
Vagi, S., On the boundary values of holomorphic functions.Rev. Un. Mat. Argentina, 25 (1970), 123–136.
Wallach, N. Induced Representations of Lie algebras II.Proc. Amer. Math. Soc., 21 (1969), 161–166.
Analytic continuation of the discrete series (I), (II). To appear.
Wolf, J., Fine structure of hermitian symmetric spaces,Symmetric Spaces, Short Lectures. Marcel Dekker, New York, 1972.
Wolf, J. &Koranyi, A., Generalized Cayley transformations of bounded symmetric domains.Amer. J. Math., 87 (1965) 899–939.
Bourbaki,Integration, Hermann, Paris, 1965, 67.
Author information
Authors and Affiliations
Additional information
Partially supported by NSF GP 28323 A3
Rights and permissions
About this article
Cite this article
Vergne, M., Rossi, H. Analytic continuation of the holomorphic discrete series of a semi-simple Lie group. Acta Math. 136, 1–59 (1976). https://doi.org/10.1007/BF02392042
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02392042