A Proof of the Lieb–Thirring Inequality via the Besicovitch Covering Lemma

We give a proof of the Lieb–Thirring inequality on the kinetic energy of orthonormal functions by using a microlocal technique, in which the uncertainty and exclusion principles are combined through the use of the Besicovitch covering lemma.

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Bibliographic Details
Published inActa mathematica vietnamica Vol. 48; no. 1; pp. 75 - 81
Main Author Nam, Phan Thành
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.04.2023
Springer Nature B.V
Subjects
Kinetic energy
Mathematics
Mathematics and Statistics
Orthonormal functions
Lieb–Thirring inequality
Besicovitch covering lemma
Semiclassical approximation
81V74
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Summary:We give a proof of the Lieb–Thirring inequality on the kinetic energy of orthonormal functions by using a microlocal technique, in which the uncertainty and exclusion principles are combined through the use of the Besicovitch covering lemma.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-022-00490-1