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Asymptotic behavior of matrix coefficients of admissible representations. (English) Zbl 0524.22014

MSC:
22E46 Semisimple Lie groups and their representations
43A90 Harmonic analysis and spherical functions
22E30 Analysis on real and complex Lie groups
17B15 Representations of Lie algebras and Lie superalgebras, analytic theory
34M99 Ordinary differential equations in the complex domain
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[1] N. Bourbaki, Éléments de mathématique. Fasc. XXX. Algèbre commutative. Chapitre 5: Entiers. Chapitre 6: Valuations , Actualités Scientifiques et Industrielles, No. 1308, Hermann, Paris, 1964. · Zbl 0205.34302
[2] N. Bourbaki, Groupes et algèbres de Lie, Chap. 1-8 , Hermann, Paris. · Zbl 0199.35203
[3] W. Casselman, Systems of analytic partial differential equations of finite codimension ,
[4] W. Casselman, Differential equations satisfied by matrix coefficients , unpublished manuscript.
[5] W. Casselman, Jacquet modules for real reductive groups , Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, 1980, pp. 557-563. · Zbl 0425.22019
[6] W. Casselman and M. S. Osborne, The restriction of admissible representations to \(\mathfrak n\) , Math. Ann. 233 (1978), no. 3, 193-198. · Zbl 0355.20041 · doi:10.1007/BF01405350 · eudml:163107
[7] E. A. Coddington and N. Levinson, Theory of ordinary differential equations , McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. · Zbl 0064.33002
[8] P. Deligne, Équations différentielles à points singuliers réguliers , Springer-Verlag, Berlin, 1970. · Zbl 0244.14004 · doi:10.1007/BFb0061194
[9] J. Dieudonné, Foundations of modern analysis , Pure and Applied Mathematics, Vol. X, Academic Press, New York, 1960. · Zbl 0100.04201
[10] R. C. Gunning and H. Rossi, Analytic functions of several complex variables , Prentice-Hall Inc., Englewood Cliffs, N.J., 1965. · Zbl 0141.08601
[11] Harish-Chandra, Some results on differential equations and their applications , Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 1763-1764. JSTOR: · Zbl 0161.33803 · doi:10.1073/pnas.45.12.1763 · links.jstor.org
[12] Harish-Chandra, Some results on differential equations , unpublished manuscript, 1960.
[13] Harish-Chandra, Differential equations and semisimple Lie groups , unpublished manuscript, 1960.
[14] S. Helgason, Differential geometry and symmetric spaces , Pure and Applied Mathematics, Vol. XII, Academic Press, New York, 1962. · Zbl 0111.18101
[15] J. Lepowsky, Algebraic results on representations of semisimple Lie groups , Trans. Amer. Math. Soc. 176 (1973), 1-44. · Zbl 0264.22012 · doi:10.2307/1996194
[16] D. Miličić, Notes on asymptotics of admissible representations of semi-simple Lie groups , unpublished manuscript, 1976.
[17] D. Miličić, Asymptotic behaviour of matrix coefficients of the discrete series , Duke Math. J. 44 (1977), no. 1, 59-88. · Zbl 0398.22022 · doi:10.1215/S0012-7094-77-04403-9
[18] Y. Nouazé and P. Gabriel, Idéaux premiers de l’algèbre enveloppante d’une algèbre de Lie nilpotente , J. Algebra 6 (1967), 77-99. · Zbl 0159.04101 · doi:10.1016/0021-8693(67)90015-4
[19] J. T. Stafford and N. R. Wallach, The restriction of admissible modules to parabolic subalgebras , Trans. Amer. Math. Soc. 272 (1982), no. 1, 333-350. · Zbl 0493.17004 · doi:10.2307/1998963
[20] V. S. Varadarajan, Harmonic analysis on real reductive groups , Springer-Verlag, Berlin, 1977. · Zbl 0354.43001 · doi:10.1007/BFb0097814
[21] N. R. Wallach, On regular singularities in several variables , · Zbl 1129.13004
[22] 1 G. Warner, Harmonic analysis on semi-simple Lie groups. I , Springer-Verlag, New York, 1972. · Zbl 0265.22020
[23] 2 G. Warner, Harmonic analysis on semi-simple Lie groups. II , Springer-Verlag, New York, 1972. · Zbl 0265.22021
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