no. 3
The principal series for a reductive symmetric space. I. H-fixed distribution vectors
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 21 (1988) no. 3, pp. 359-412 
@article{ASENS_1988_4_21_3_359_0,
     author = {van den Ban, E. P.},
     title = {The principal series for a reductive symmetric space. {I.} $H$-fixed distribution vectors},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {359--412},
     year = {1988},
     publisher = {Elsevier},
     volume = {Ser. 4, 21},
     number = {3},
     doi = {10.24033/asens.1562},
     mrnumber = {90a:22016},
     zbl = {0714.22009},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/asens.1562/}
}
TY  - JOUR
AU  - van den Ban, E. P.
TI  - The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1988
SP  - 359
EP  - 412
VL  - 21
IS  - 3
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.24033/asens.1562/
DO  - 10.24033/asens.1562
LA  - en
ID  - ASENS_1988_4_21_3_359_0
ER  - 
%0 Journal Article
%A van den Ban, E. P.
%T The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors
%J Annales scientifiques de l'École Normale Supérieure
%D 1988
%P 359-412
%V 21
%N 3
%I Elsevier
%U https://www.numdam.org/articles/10.24033/asens.1562/
%R 10.24033/asens.1562
%G en
%F ASENS_1988_4_21_3_359_0
van den Ban, E. P. The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 21 (1988) no. 3, pp. 359-412. doi: 10.24033/asens.1562

[Ba 86] E. P. Van Den Ban, A Convexity Theorem for Semisimple Symmetric Spaces (Pac. J. Math., Vol. 124, 1986, pp. 21-55). | Zbl | MR

[Ba 87 I] E. P. Van Den Ban, Invariant Differential Operators on a Semisimple Symmetric Space and Finite Multiplicities in a Plancherel Formula (Ark. för Mat., Vol. 25, 1987, pp. 175-187). | Zbl | MR

[Ba 87 II] E. P. Van Den Ban, Asymptotic Behaviour of Matrix Coefficients Related to Reductive Symmetric Spaces (Proc. Kon. Ned. Akad. Wet., Ser. A, Vol. 90, 1987, pp. 225-249). | Zbl | MR

[Ba 88] E. P. Van Den Ban, The Principal Series for a Reductive Symmetric Space II. Eisenstein Integrals, in preparation.

[Be 57] M. Berger, Les espaces symétriques non-compacts (Ann. scient. Ec. Norm. Sup., Vol. 74, 1957, pp. 85-117). | Zbl | MR | Numdam

[B 72] I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter (Funct. Anal. and its Applic., Vol. 6, 1972, pp. 273-285). | Zbl | MR

[B-G 69] I. N. Bernstein and I. S. Gelfand, Meromorphic Property of the Function Pλ (Funct. Anal. and its Applic., Vol. 3, 1969, pp. 68-69).

[Br 56] F. Bruhat, Sur les représentations induites des groupes de Lie (Bull. Soc. Math. France, Vol. 84, 1956, pp. 97-205). | Zbl | MR | Numdam

[D 85] P. Delorme, Injection de modules sphériques pour les espaces symétriques réductifs dans certaines représentations induites (Proceedings Marseille-Luminy 1985, LNM 1243), Springer-Verlag, 1987, pp. 108-134. | Zbl | MR

[DP 86] G. Van Dijk and M. Poel, The Plancherel Formula for the Pseudo-Riemannian Space SL (n, ℝ)/G1 (n - 1, ℝ) (Comp. Math., Vol. 58, 1986, pp. 371-397). | Zbl | MR | Numdam

[Fa 79] J. Faraut, Distributions sphériques sur les espaces hyperboliques (J. Math. Pures Appl., Vol. 58, 1979, pp. 369-444). | Zbl | MR

[FJ 86] M. Flensted-Jensen, Analysis on non-Riemannian Symmetric Spaces (A.M.S. Regional Conference Series 61, 1986). | Zbl | MR

[HC 58 I, II] Harish-Chandra, Spherical Functions on a Semisimple Lie Group I, II (Amer. J. of Math., Vol. 80, 1958, pp. 241-310 and pp. 553-613). | Zbl | MR

[HC 75] Harish-Chandra, Harmonic Analysis on Real Reductive Groups I. The theory of the constant term (J. Funct. Anal., Vol. 19, 1975, pp. 103-204). | Zbl | MR

[HC 76] Harish-Chandra, Harmonic Analysis on Real Reductive Groups II. Wave Packets in the Schwartz Space (Invent. Math., Vol. 36, 1979, pp. 1-55). | Zbl | MR

[HC 76 II] Harish-Chandra, Harmonic Analysis on Real Reductive Groups III. The Maass-Selberg Relations and the Plancherel Formula (Ann. of Math., Vol. 104, 1976, pp. 117-201). | Zbl | MR

[He 84] S. Helgason, Groups and Geometric Analysis, Academic Press, 1984. | Zbl | MR

[Hör 83] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer-Verlag, 1983.

[KKMOOT 78] M. Kashiwara, A. Kowata, K. Minemura, K. Okamoto, T. Oshima and M. Tanaka, Eigenfunctions of Invariant Differential Operators on a Symmetric Space. (Ann. of Math., Vol. 107, 1978, pp. 1-39). | Zbl | MR

[K-S 80] A. W. Knapp and E. M. Stein, Intertwining Operators for Semisimple Groups (Ann. of Math., Vol. 93, 1971, pp. 489-578). | Zbl | MR

[K-S 80] A. W. Knapp and E. M. Stein, Intertwining Operators for Semisimple Groups, II (Invent. Math., Vol. 60, 1980, pp. 9-84). | Zbl | MR

[Kn 82] A. W. Knapp, Commutativity of Intertwining Operators for Semisimple Groups (Comp. Math., Vol. 46, 1982, pp. 33-84). | Zbl | MR | Numdam

[Kom 67] H. Komatsu, Projective and Injective Limits of Weakly Compact Sequences of Locally Convex Spaces (J. Math. Soc. Japan, Vol. 19, 1967, pp. 366-383). | Zbl | MR

[Ko-Ra 71] B. Kostant and S. Rallis, Orbits and Representations Associated with Symmetric Spaces (Amer. J. Math., Vol. 93, 1971, pp. 753-809). | Zbl | MR

[Ma 79] T. Matsuki, The Orbits of Affine Symmetric Spaces under the Action of Minimal Parabolic Subgroups (J. Math. Soc. Japan, Vol. 31, 1979, pp. 331-357). | Zbl | MR

[Ma 82] T. Matsuki, Orbits on Affine Symmetric Spaces under the Action of Parabolic Subgroups (Hiroshima Math. J. Vol. 12, 1982, pp. 307-320). | Zbl | MR

[O1 87] G. Olafsson, Fourier and Poisson Transformation Associated to a Semisimple Symmetric Space (Invent. Math., Vol. 90, 1987, pp. 605-629). | Zbl | MR

[Os 79] T. Oshima, Poisson Transformations on Affine Symmetric Spaces (Proc. Japan Acad., Vol. 55, Série A, 1979, pp. 323-327). | Zbl | MR

[O-S 80] T. Oshima and J. Sekiguchi, Eigenspaces of Invariant Differential Operators on an Affine Symmetric Space (Invent. Math., Vol. 57, 1980, pp. 1-81). | Zbl | MR

[Pe 75] R. Penney, Abstract Plancherel Theorems and a Frobenius Reciprocity Theorem (J. of Funct. Anal., Vol. 18, 1975, pp. 177-190). | Zbl | MR

[Ro 78] W. Rossmann, Analysis on Real Hyperbolic Spaces (J. Funct. Anal., Vol. 30, 1978, pp. 448-477). | Zbl | MR

[Ro 79] W. Rossmann, The Structure of Semisimple Symmetric Spaces (Can. J. Math., Vol. 31, 1979, pp. 157-180). | Zbl | MR

[S 71] G. Schiffmann, Intégrales d'entrelacement et fonctions de Whittaker (Bull. Soc. Math., France, Vol. 99, 1971, pp. 3-72). | Zbl | MR | Numdam

[Schl 84] H. Schlichtkrull, Hyperfunctions and Harmonic Analysis on Symmetric Spaces, Birkhöuser, 1984. | Zbl | MR

[Schw 50] L. Schwartz, Théorie des distributions, Tome I, Hermann, 1950. | Zbl | MR

[Str 73] R. S. Strichartz, Harmonic analysis on hyperboloids (J. Funct. Anal., Vol. 12, 1973, pp. 341-383). | Zbl | MR

[Va 74] V. S. Varadarajan, Lie Groups, Lie Algebras, and their Representations, Prentice Hall, 1974. | Zbl | MR

[Va 77] V. S. Varadarajan, Harmonic Analysis on Real Reductive Groups (Lecture Notes 576), Springer-Verlag, 1977. | Zbl | MR

[Vo 81] D. A. Vogan, Representations of Real Reductive Lie Groups, (P.M. 15), Birkhöuser, Boston, 1981. | Zbl | MR

[War 72] G. Warner, Harmonic Analysis on Semi-Simple Lie Groups I, Springer-Verlag, 1972. | Zbl

Cité par Sources :