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The heat kernel on H-type groups
Author(s):
Qiaohua
Yang;
Fuliu
Zhu
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1457-1464.
MSC (2000):
Primary 22E25, 35A08
Posted:
December 21, 2007
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Abstract:
In this paper we present an explicit calculation of the heat kernel for the sub-Laplacian on an H-type group  by using irreducible unitary representations of  and the heat kernel for the associated Hermite operator.
References:
-
- 1.
- F. Astengo, M. Cowling, B. Di Blasio, M. Sundari, Hardy's uncertainty principle on certain Lie groups, J. London Math. Soc., 62 (2000), 461-472. MR 1783638 (2002b:22018)
- 2.
- R. Beals, B. Gaveau, P. Greiner, Complex Hamiltonian mechanics and parametrices for subelliptic Laplacians, Bull. Sci. Math. 121 (1997), 1-36. MR 1431098 (98b:35032a)
- 3.
- A. Bonfiglioli, F. Uguzzoni, Nonlinear Liouville theorems for some critical problems on H-type groups, J. Functional Analysis, 207 (2004), 161-215. MR 2027639 (2004k:35057)
- 4.
- D.C. Chang, J.Z. Tie, A note on Hermite and subelliptic operators, Acta Math. Sin., 21 (2005), 803-818. MR 2156956 (2006e:42013)
- 5.
- L.J. Corwin, F.P. Greenleaf, Representations of nilpotent Lie groups and their applications. 1: Basic theory and examples, Cambridge Studies in Advanced Mathematics 18, Cambridge University Press, 1990. MR 1070979 (92b:22007)
- 6.
- J. Cygan, Heat kernels for class
 nilpotent groups, Studia Math., 64 (1979), 227-238. MR 544727 (82b:22016) - 7.
- B. Gaveau, Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents, Acta Math., 139 (1977), 95-153. MR 0461589 (57:1574)
- 8.
- L. Hörmander, Hypoelliptic second order differential equations, Acta Math., Uppsala, 119 (1967), 147-171. MR 0222474 (36:5526)
- 9.
- A. Hulanicki, The distribution of energy of the Brownian motion in the Gaussian field and analytic hypoellipticity of certain subelliptic operators on the Heisenberg group, Studia Math., 56 (1976), 165-173. MR 0418257 (54:6298)
- 10.
- A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms, Trans. Amer. Math. Soc., 258 (1980), 147-153. MR 554324 (81c:58059)
- 11.
- W. Staubach, Wiener path integrals and the fundamental solution for the Heisenberg Laplacian, J. d'Analyse Math., 91 (2003), 389-400. MR 2037416 (2005m:35052)
- 12.
- S. Thangavelu, An introduction to the uncertainty principle: Hardy's theorem on Lie groups, Progress in Mathematics, 217, Birkh
 user, Boston, 2004. MR 2008480 (2004j:43007) - 13.
- Fuliu Zhu, The heat kernel and the Riesz transforms on the quaternionic Heisenberg groups, Pacific J. Math. 209 (2003), 175-199. MR 1973940 (2004e:43013)
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Additional Information:
Qiaohua
Yang
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People's Republic of China
Address at time of publication:
Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, People's Republic of China
Email:
qaohyang2465@yahoo.com.cn
Fuliu
Zhu
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People's Republic of China
Email:
flzhu@whu.edu.cn
DOI:
10.1090/S0002-9939-07-09257-X
PII:
S 0002-9939(07)09257-X
Keywords:
H-type groups,
sub-Laplacian,
heat kernel,
Hermite operator
Received by editor(s):
March 30, 2006
Posted:
December 21, 2007
Additional Notes:
The first author was supported by the National Science Foundation of China under grant number 10571044.
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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