Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T21:30:29.345Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimates for the Heat Kernel on SL(n,R)/ SO(n)

Published online by Cambridge University Press:  20 November 2018

P. Sawyer
P. Sawyer*
Affiliation:
Department of Mathematics and Computer Science, Laurentian University, Sudbury, Ontario, P3E 5C6 e-mail: sawyer@ramsey.cs.laurentian.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [1], Jean-Philippe Anker conjectures an upper bound for the heat kernel of a symmetric space of noncompact type. We show in this paper that his prediction is verified for the space of positive definite n × n real matrices.

Keywords

58G3053C3558G11
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 360 - 373
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Anker, Jean-Philippe, Le noyau de la chaleur sur les espaces symétriques U(p, q)/U(p) ₓ U(q), Lecture Notes in Math. 1359, Springer Verlag, New York, 1988. 60–82.Google Scholar
2. Anker, Jean-Philippe, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J. (2) 65(1992), 257–297.Google Scholar
3. Chayet, Maurice, Some general estimates for the heat kernel on a symmetric space and related problems of integral geometry, Thesis, McGill University, 1990. 1–76.Google Scholar
4. Davies, E.B., Heat kernels and spectral theory, Cambridge Univ. Press, 1989.Google Scholar
5. Gangolli, R., Asymptotic behaviour of spectra of compact quotients of certain symmetric spaces, Acta Math. 121(1968), 151–192.Google Scholar
6. Flensted-Jensen, Mogens, Spherical functions on a real semisimple Lie group. A method of reduction to the complex case, J. Funct. Anal. 30 1948, 106–146.Google Scholar
7. Sawyer, Patrice, The heat equation on spaces of positive definite matrices, Canad. J. Math. (3) 44(1992), 624–651.Google Scholar
8. Sawyer, Patrice, On an upper bound for the heat kernel on SU*(2n)/Sp(n, ), Canad. Bull. Math. (3) 37(1994), 408–418.Google Scholar
9. Sawyer, Patrice, Spherical functions on symmetric cones, Trans. Amer. Math. Soc. (1995), 1–15.Google Scholar