Improved Berezin-Li-Yau inequalities with a remainder term
T. Weidl. Spectral theory of differential operators, Volume 225 von Amer. Math. Soc. Transl. Ser. 2, Amer. Math. Soc., Providence, RI, (2008)
DOI: 10.1090/trans2/225/17
Zusammenfassung
We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(Łambda-łambda_k)_+^\sigma$ of the eigenvalues $łambda_k$ of the Dirichlet Laplacian in a domain if $\sigma3/2$. It contains a correction term of the order of the standard second term in the Weyl asymptotics. The result is based on an application of sharp Lieb-Thirring inequalities with operator valued potential to spectral estimates of the Dirichlet Laplacian in domains.
%0 Book Section
%1 MR2509788
%A Weidl, Timo
%B Spectral theory of differential operators
%D 2008
%I Amer. Math. Soc., Providence, RI
%K Berezin-Li-Yau Improved Weidl a from:elkepeter inequalities remainder term with
%P 253--263
%R 10.1090/trans2/225/17
%T Improved Berezin-Li-Yau inequalities with a remainder term
%U https://doi.org/10.1090/trans2/225/17
%V 225
%X We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(Łambda-łambda_k)_+^\sigma$ of the eigenvalues $łambda_k$ of the Dirichlet Laplacian in a domain if $\sigma3/2$. It contains a correction term of the order of the standard second term in the Weyl asymptotics. The result is based on an application of sharp Lieb-Thirring inequalities with operator valued potential to spectral estimates of the Dirichlet Laplacian in domains.
@incollection{MR2509788,
abstract = {We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(\Lambda-\lambda_k)_+^\sigma$ of the eigenvalues $\lambda_k$ of the Dirichlet Laplacian in a domain if $\sigma\geq 3/2$. It contains a correction term of the order of the standard second term in the Weyl asymptotics. The result is based on an application of sharp Lieb-Thirring inequalities with operator valued potential to spectral estimates of the Dirichlet Laplacian in domains. },
added-at = {2022-03-30T16:35:09.000+0200},
author = {Weidl, Timo},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/255b53c5ecef089ad7c993cb0ae7b04f2/mathematik},
booktitle = {Spectral theory of differential operators},
doi = {10.1090/trans2/225/17},
interhash = {b0b50f4bb237f394c9f446b269b0356e},
intrahash = {55b53c5ecef089ad7c993cb0ae7b04f2},
keywords = {Berezin-Li-Yau Improved Weidl a from:elkepeter inequalities remainder term with},
mrclass = {35P15 (35J05 35J10 35P20 47A10 47F05)},
mrnumber = {2509788},
mrreviewer = {G\"{u}nter Berger},
pages = {253--263},
publisher = {Amer. Math. Soc., Providence, RI},
series = {Amer. Math. Soc. Transl. Ser. 2},
timestamp = {2023-04-21T12:15:41.000+0200},
title = {Improved {B}erezin-{L}i-{Y}au inequalities with a remainder term},
url = {https://doi.org/10.1090/trans2/225/17},
volume = 225,
year = 2008
}
