Schrödinger operators : eigenvalues and Lieb-Thirring inequalities
著者
書誌事項
Schrödinger operators : eigenvalues and Lieb-Thirring inequalities
（Cambridge studies in advanced mathematics, 200）
Cambridge University Press, 2023
- : hardback
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注記
Includes bibliographical references (p. 471-503) and index
内容説明・目次
内容説明
The analysis of eigenvalues of Laplace and Schroedinger 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 Schroedinger 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.
目次
- Overview
- Part I. Background Material: 1. Elements of operator theory
- 2. Elements of Sobolev space theory
- Part II. The Laplace and Schroedinger Operators: 3. The Laplacian on a domain
- 4. The Schroedinger operator
- Part III. Sharp Constants in Lieb-Thirring Inequalities:5. Sharp Lieb-Thirring inequalities
- 6. Sharp Lieb-Thirring inequalities in higher dimensions
- 7. More on sharp Lieb-Thirring inequalities
- 8. More on the Lieb-Thirring constants
- References
- Index.
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