256 research outputs found
New bounds on the Lieb-Thirring constants
Improved estimates on the constants , for ,
in the inequalities for the eigenvalue moments of Schr\"{o}dinger
operators are established
Geometrical Versions of improved Berezin-Li-Yau Inequalities
We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary
bounded, open set in , . In particular, we derive upper bounds
on Riesz means of order , that improve the sharp Berezin
inequality by a negative second term. This remainder term depends on geometric
properties of the boundary of the set and reflects the correct order of growth
in the semi-classical limit. Under certain geometric conditions these results
imply new lower bounds on individual eigenvalues, which improve the Li-Yau
inequality.Comment: 18 pages, 1 figur
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