Keywords
- Symmetric Space
- Invariant Differential Operator
- Nous Allons
- Complex Grassmann Manifold
- Prolongeant Analytiquement
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliographie
J.-Ph. Anker: La forme exacte de l'estimation fondamentale de Harish-Chandra, C. R. Acad. Sci. Paris 305-série I (1987), 371–374.
J.-Ph. Anker & N. Lohoué: Multiplicateurs sur certains espaces symétriques, Amer. J. Math. 108 (1986), 1303–1354.
K. Aomoto: Sur les transformations d'horisphère et les intégrales qui s'y rattachent, J. Fac. Sci. Univ. Tokyo 14 (1967), 1–23.
R. Azencott & al.: Géodésiques et diffusions en temps petit, Astérisque 84–85, Soc. Math. France (1981).
R. J. Beerends: On the Abel transform and its inversion, Thèse, Univ. Leiden (1986).
F. A. Berezin & F. I. Karpelevič: "Fonctions sphériques zonales et opérateurs de Laplace sur certains espaces symétriques" (en russe), Dokl. Akad. Nauk. USSR 118 (1958), 9–12.
I. Chavel: Eigenvalues in Riemannian Geometry, Academic Press (1984).
J. Cheeger, M. Gromov & M. E. Taylor: Finite propagation speed, kernel estimates for functions of the Laplace operator and the geometry of complete Riemannian manifolds, J. Diff. Geometry 17 (1982), 15–53.
S. Cheng, P. Li & S.-T. Yau: On the upper estimate of the heat kernel on a complete Riemannian manifold, Amer. J. Math. 103 (1981), 1021–1063.
A. Debiard & B. Gaveau: Analysis on root systems, Prépublication (1986).
A. Debiard & B. Gaveau: Noyaux de la chaleur pour certaines équations hypergéométriques et application aux espaces symétriques de rang 1, C. R. Acad. Sci. Paris 303-Série I (1986), 849–852.
A. Debiard & B. Gaveau: Noyaux de la chaleur, systèmes de racines, et espaces symétriques de type B2, C. R. Acad. Sci. Paris 303-série I (1986), 951–953.
A. Debiard & B. Gaveau: Noyaux de la chaleur de certaines équations aux dérivées partielles à singularité régulière et applications à certains espaces symétriques, C. R. Acad. Sci. Paris 304-série I (1987), 131–133.
A. Debiard, B. Gaveau & E. Mazet: Théorèmes de Comparaison en Géométrie Riemannienne, Publ. R. I. M. S. Kyoto Univ. 12 (1976), 391–425.
L. D. Èskin: The Heat Equation and the Weierstrass Transform on Certain Riemannian Spaces, Amer. Math. Soc. Transl. 75 (1968), 239–255.
M. Flensted-Jensen: Spherical functions on a real semisimple Lie group. A method of reduction to the complex case, J. Funct. Anal. 30 (1978), 106–146.
R. Gangolli: Asymptotic behaviour of spectra of compact quotients of certain symmetric spaces, Acta Math. 121 (1968), 151–192.
S. G. Gindikin & F. I. Karpelevič: Plancherel measure for Riemannian symmetric spaces of nonpositive curvature, Soviet Math. Dokl. 3 (1962), 962–965.
R. Godement: Introduction aux travaux de A. Selberg, Séminaire Bourbaki 144 (1957).
A. Hba: Analyse harmonique sur SL (3, IH), C. R. Acad. Sci. Paris 305-série I (1987), 77–80.
S. Helgason: Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press (1978).
S. Helgason: Groups and Geometric Analysis, Academic Press (1984).
B. Hoogenboom: Spherical functions and invariant differential operators on complex Grassmann manifolds, Ark. Mat. 20 (1982), 69–85.
L. Hörmander: An Introduction to Complex Analysis in Several Variables, North-Holland (1973).
T. H. Koornwinder: A new proof of a Paley-Wiener type theorem for the Jacobi transform, Ark. Mat. 13 (1975), 145–159.
T. H. Koornwinder: Jacobi Functions and Analysis on Noncompact Semisimple Groups, dans "Special Functions: Group Theoretical Aspects and Applications", R. A. Askey & al. (eds.), Reidel (1984), 1–85.
P. Li & S.-T. Yau: On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153–201.
N. Lohoué & Th. Rychener: Some Function Spaces on Symmetric Spaces Related to Convolution Operators, Prépublication Orsay (1978).
N. Lohoué & Th. Rychener: Die Resolvente von Δ auf symmetrischen Räumen vom nichtkompakten Typ, Comment. Math. Helv. 57 (1982), 445–468.
N. Lohoué & Zhu Fu Liu: Estimation faible de certaines fonctions maximales, C. R. Acad. Sci. Paris 302-série I (1986), 303–305.
H. P. McKean: An Upper Bound to the Spectrum of Δ on a Manifold of Negative Curvature, J. Diff. Geometry 4 (1970), 359–366.
Ch. Meaney: The Inverse Abel Transform for SU(p, q), Ark. Mat. 24 (1986), 131–140.
F. Rouvière: Sur la transformation d'Abel des groupes de Lie semisimples de rang un, Ann. Scuola Norm. Sup. Pisa 10 (1983), 263–290.
R. J. Stanton & P. A. Tomas: Expansions for spherical functions on noncompact symmetric spaces, Acta Math. 140 (1978), 251–276.
R. S. Strichartz: Analysis of the Laplacian on the Complete Riemannian Manifold, J. Funct. Anal. 52 (1983), 48–79.
R. Takahashi: Sur les représentations unitaires des groupes de Lorentz généralisés, Bull. Soc. Math. France 91 (1963), 289–433.
R. Takahashi: Fonctions sphériques zonales sur U(n, n+k; IF), dans "Séminaire d'Analyse Harmonique 1976–1977", Faculté des Sciences de Tunis (1977).
V. S. Varadarajan: Asymptotic properties of eigenvalues and eigenfunctions of invariant differential operators on symmetric and locally symmetric spaces, dans "Lie Groups Representations III", R. Herb & al. (eds.), Lect. Notes Math. 1077, Springer (1984), 396–436.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Anker, JP. (1988). Le noyau de la chaleur sur les espaces symetriques U(p,q)/U(p)×U(q). In: Eymard, P., Pier, JP. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086588
Download citation
DOI: https://doi.org/10.1007/BFb0086588
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50524-2
Online ISBN: 978-3-540-46032-9
eBook Packages: Springer Book Archive
