Equivalence of Sobolev inequalities and Lieb-Thirring inequalities

Details Equivalence of Sobolev inequalities and Lieb-Thirring inequalities Equivalence of Sobolev inequalities and Lieb-Thirring inequalities

2009-09-29

arxiv.org/abs/0909.5449v1

Mathematics

Spectral Theory

13 pages; contribution to the proceedings of the XVI International Congress on Mathematical Physics, Prague, 2009

Scientific paper

We show that, under very general definitions of a kinetic energy operator
$T$, the Lieb-Thirring inequalities for sums of eigenvalues of $T-V$ can be
derived from the Sobolev inequality appropriate to that choice of $T$.

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