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The subelliptic heat kernels on SL(2,R) and on its universal covering SL(2,R)˜: integral representations and some functional inequalities

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBONNEFONT, Michel
dc.date.accessioned2024-04-04T02:22:51Z
dc.date.available2024-04-04T02:22:51Z
dc.date.issued2012
dc.identifier.issn0926-2601
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189681
dc.description.abstractEnIn 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 its universal covering. First, we derive an integral representation for these heat kernels. These expressions allow us to obtain some asymptotics in small time of the heat kernels and give us a way to compute the subriemannian distances. 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.
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enThe subelliptic heat kernels on SL(2,R) and on its universal covering SL(2,R)˜: integral representations and some functional inequalities
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Géométrie différentielle [math.DG]
bordeaux.journalPotential Analysis
bordeaux.page36, no. 2, 275-300.
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00779378
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00779378v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Potential%20Analysis&rft.date=2012&rft.spage=36,%20no.%202,%20275-300.&rft.epage=36,%20no.%202,%20275-300.&rft.eissn=0926-2601&rft.issn=0926-2601&rft.au=BONNEFONT,%20Michel&rft.genre=article


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