Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique

Jacques Faraut

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2002)

  • Volume: 13, Issue: 3-4, page 233-241
  • ISSN: 1120-6330

Abstract

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A Gutzmer formula for the complexification of a Riemann symmetric space. We consider a complex manifold Ω and a real Lie group G of holomorphic automorphisms of Ω . The question we study is, for a holomorphic function f on Ω , to evaluate the integral of f 2 over a G -orbit by using the harmonic analysis of G . When Ω is an annulus in the complex plane and G the rotation group, it is solved by a classical formula which is sometimes called Gutzmer’s formula. We establish a generalization of it when Ω is a G -invariant domain in the complexification of a Riemannian symmetric space G / K .

How to cite

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Faraut, Jacques. "Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.3-4 (2002): 233-241. <http://eudml.org/doc/252402>.

@article{Faraut2002,
author = {Faraut, Jacques},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Symmetric space; Spherical function; Gutzmer formula},
language = {fre},
month = {12},
number = {3-4},
pages = {233-241},
publisher = {Accademia Nazionale dei Lincei},
title = {Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique},
url = {http://eudml.org/doc/252402},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Faraut, Jacques
TI - Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/12//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 3-4
SP - 233
EP - 241
LA - fre
KW - Symmetric space; Spherical function; Gutzmer formula
UR - http://eudml.org/doc/252402
ER -

References

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  1. Akhiezer, D.N. - Gindikin, S.G., On Stein extensions of real symmetric spaces. Math. Ann., 286, 1990, 1-12. Zbl0681.32022MR1032920DOI10.1007/BF01453562
  2. Geatti, L., Invariant domains in the complexification of a non-compact Riemannian symmetric space. Preprint, 2001. Zbl1018.32030
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  4. Krötz, B. - Stanton, R.J., Holomorphic aspects of representations: (I) automorphic functions. Preprint, 2001. Zbl1053.22009
  5. Lassalle, M., Séries de Laurent des fonctions holomorphes dans la complexification d’un espace symétrique compact. Ann. Scient. Éc. Norm. Sup., 11, 1978, 167-210. Zbl0452.43011MR510548
  6. Lassalle, M.,L’espace de Hardy d’un domaine de Reinhardt généralisé. J. Funct. Anal., 60, 1985, 309-340. Zbl0578.32009MR780501DOI10.1016/0022-1236(85)90043-6
  7. Paley, R.E. - Wiener, N., Fourier transforms in the complex domain. A.M.S., 1934. Zbl0123.30104
  8. Valiron, G., Théorie des fonctions. Masson, 1966. Zbl0028.20801

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