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Heat kernels of metric trees and applications

Frank, Rupert L. and Kovařík, Hynek (2013) Heat kernels of metric trees and applications. SIAM Journal on Mathematical Analysis, 45 (3). pp. 1027-1046. ISSN 0036-1410. doi:10.1137/120886297. https://resolver.caltech.edu/CaltechAUTHORS:20130815-102433930

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Abstract

We consider the heat semigroup generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue estimates for Schrödinger operators on metric trees.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1108.6145arXivDiscussion Paper
http://dx.doi.org/ 10.1137/120886297 DOIArticle
http://epubs.siam.org/doi/abs/10.1137/120886297PublisherArticle
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2013 SIAM. Received by the editors July 27, 2012; accepted for publication December 14, 2012; published electronically May 7, 2013. This author’s work was supported through DFG grant FR 2664/1-1 and U.S. NSF grant PHY-0652854. This author was partially supported by the MIUR-PRIN08 grant for the project ”Trasporto ottimo di massa, disuguaglianze geometriche e funzionali e applicazioni.”
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)FR 2664/1-1
NSFPHY-0652854
MIUR-PRIN08 GrantUNSPECIFIED
Subject Keywords:heat kernel, metric tree, eigenvalue estimate, Sobolev inequality
Issue or Number:3
Classification Code:AMS subject classifications: 47D06, 47D08, 34B45
DOI:10.1137/120886297
Record Number:CaltechAUTHORS:20130815-102433930
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130815-102433930
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39949
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Aug 2013 22:57
Last Modified:09 Nov 2021 23:48

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