A Note On The Eigenvalues Of Compact Operators
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Advanced Real Analysis
Author: Anthony W. Knapp
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-07-11
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities
Author: Rupert L. Frank
language: en
Publisher: Cambridge University Press
Release Date: 2022-11-17
The analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students, and includes an ample amount of background material on the spectral theory of linear operators in Hilbert spaces and on Sobolev space theory. Of particular interest is a family of inequalities by Lieb and Thirring on eigenvalues of Schrödinger operators, which they used in their proof of stability of matter. The final part of this book is devoted to the active research on sharp constants in these inequalities and contains state-of-the-art results, serving as a reference for experts and as a starting point for further research.