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On the remainder term of the Berezin inequality on a convex domainPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2017 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 145, no 5, p. 2167-2181Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Mathematical Society (AMS), 2017. Vol. 145, no 5, p. 2167-2181
##### Keywords [en]

Dirichlet-Laplace operator, semi-classical estimates, Berezin-Li-Yau inequality
##### National Category

Mathematical Analysis
##### Identifiers

URN: urn:nbn:se:kth:diva-205425DOI: 10.1090/proc/13386ISI: 000395809900031Scopus ID: 2-s2.0-85013627273OAI: oai:DiVA.org:kth-205425DiVA, id: diva2:1097234
#####

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##### Note

##### In thesis

We study the Dirichlet eigenvalues of the Laplacian on a convex domain in R-n, with n >= 2. In particular, we generalize and improve upper bounds for the Riesz means of order sigma >= 3/2 established in an article by Geisinger, Laptev and Weidl. This is achieved by refining estimates for a negative second term in the Berezin inequality. The obtained remainder term reflects the correct order of growth in the semi-classical limit and depends only on the measure of the boundary of the domain. We emphasize that such an improvement is for general Omega subset of R-n not possible and was previously known to hold only for planar convex domains satisfying certain geometric conditions. As a corollary we obtain lower bounds for the individual eigenvalues lambda(k), which for a certain range of k improves the Li-Yau inequality for convex domains. However, for convex domains one can use different methods to obtain even stronger lower bounds for lambda(k)

QC 20170522

Available from: 2017-05-22 Created: 2017-05-22 Last updated: 2019-05-02Bibliographically approved1. Asymptotic and universal spectral estimates with applications in many-body quantum mechanics and spectral shape optimization$(function(){PrimeFaces.cw("OverlayPanel","overlay1313048",{id:"formSmash:j_idt828:0:j_idt832",widgetVar:"overlay1313048",target:"formSmash:j_idt828:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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