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Elsevier, Journal of Functional Analysis, 1(238), p. 193-220, 2006

DOI: 10.1016/j.jfa.2005.11.008

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Lieb–Thirring type inequalities and Gagliardo–Nirenberg inequalities for systems

Journal article published in 2006 by Jean Dolbeault ORCID, Patricio Felmer, Michael Loss, Eric Paturel
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

New references added We prove a Lieb-Thirring type inequality for potentials such that the associated Schrödinger operator has a pure discrete spectrum made of an unbounded sequence of eigenvalues. This inequality is equivalent to a generalized Gagliardo-Nirenberg inequality for systems. As a special case, we prove a logarithmic Sobolev inequality for infinite systems of mixed states. Optimal constants are determined and free energy estimates in connection with mixed states representations are also investigated. oui