The Subelliptic Heat Kernels on SL(2, ℝ) and on its Universal Covering : Integral Representations and Some Functional Inequalities
In this paper, we study a subelliptic heat kernel on the Lie group SL (2, ℝ) and on its universal covering . The subelliptic structure on SL (2,ℝ) comes from the fibration SO (2)→ SL (2,ℝ) → H 2 and it can be lifted to . First, we derive an integral representation for these heat kernels. These expre...
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Published in | Potential analysis Vol. 36; no. 2; pp. 275 - 300 |
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Main Author | |
Format | Journal Article |
Language | English |
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Dordrecht
Springer Netherlands
2012
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Abstract | In this paper, we study a subelliptic heat kernel on the Lie group
SL
(2, ℝ) and on its universal covering
. The subelliptic structure on
SL
(2,ℝ) comes from the fibration
SO
(2)→
SL
(2,ℝ) →
H
2
and it can be lifted to
. First, we derive an integral representation for these heat kernels. These expressions allow us to obtain some asymptotics in small times of the heat kernels and give us a way to compute the subriemannian distance. Then, we establish some gradient estimates and some functional inequalities like a Li-Yau type estimate and a reverse Poincaré inequality that are valid for both heat kernels. |
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AbstractList | In this paper, we study a subelliptic heat kernel on the Lie group
SL
(2, ℝ) and on its universal covering
. The subelliptic structure on
SL
(2,ℝ) comes from the fibration
SO
(2)→
SL
(2,ℝ) →
H
2
and it can be lifted to
. First, we derive an integral representation for these heat kernels. These expressions allow us to obtain some asymptotics in small times of the heat kernels and give us a way to compute the subriemannian distance. Then, we establish some gradient estimates and some functional inequalities like a Li-Yau type estimate and a reverse Poincaré inequality that are valid for both heat kernels. |
Author | Bonnefont, Michel |
Author_xml | – sequence: 1 givenname: Michel surname: Bonnefont fullname: Bonnefont, Michel email: michel.bonnefont@math.u-bordeaux1.fr organization: Institut de Mathématiques de Bordeaux, CNRS UMR, Université Bordeaux 1 |
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DOI | 10.1007/s11118-011-9230-4 |
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Snippet | In this paper, we study a subelliptic heat kernel on the Lie group
SL
(2, ℝ) and on its universal covering
. The subelliptic structure on
SL
(2,ℝ) comes from... |
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SourceType | Publisher |
StartPage | 275 |
SubjectTerms | Functional Analysis Geometry Mathematics Mathematics and Statistics Potential Theory Probability Theory and Stochastic Processes |
Title | The Subelliptic Heat Kernels on SL(2, ℝ) and on its Universal Covering : Integral Representations and Some Functional Inequalities |
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