Weak Poincaré inequalities in the absence of spectral gaps

Ben-Artzi, Jonathan ORCID: https://orcid.org/0000-0001-6184-9313 and Einav, Amit 2020. Weak Poincaré inequalities in the absence of spectral gaps. Annales Henri Poincaré 21 , pp. 359-375. 10.1007/s00023-019-00858-4

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Abstract

For generators of Markov semigroups which lack a spectral gap, it is shown how bounds on the density of states near zero lead to a so-called 'weak Poincaré inequality' (WPI), originally introduced by Liggett [Ann. Probab., 1991]. Applications to general classes of constant coefficient pseudodifferential operators are studied. Particular examples are the heat semigroup and the semigroup generated by the fractional Laplacian in the whole space, where the optimal decay rates are recovered. Moreover, the classical Nash inequality appears as a special case of the WPI for the heat semigroup.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Publisher:	Springer
ISSN:	1424-0637
Funders:	EPSRC
Date of First Compliant Deposit:	30 September 2019
Date of Acceptance:	9 October 2019
Last Modified:	05 May 2023 14:54
URI:	https://orca.cardiff.ac.uk/id/eprint/125720

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