Lieb-Thirring bounds and other inequalities for orthonormal functions
MATHEMATICAL PICTURE LANGUAGE
Rupert Frank - Ludwig-Maximilians-Universität Münchens
Lieb-Thirring inequalities are a mathematical expression of the uncertainty and exclusion principles in quantum mechanics. They were introduced by Lieb and Thirring in 1975 in their proof of stability of matter and have since played an important role in several areas of analysis and mathematical physics. We provide a gentle introduction to classical aspects of this subject and we also present some newer developments, concerning extensions of several inequalities in harmonic analysis to the setting of families of orthonormal functions.