Schrodinger Operators: Eigenvalues and LiebThirring Inequalities
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Schrodinger Operators: Eigenvalues and LiebThirring Inequalities by Timo Weidl
Eigenvalues of Laplace and Schrodinger operators play a fundamental role in many applications in mathematics and physics. This graduate-level book is devoted to their qualitative and quantitative mathematical analysis. It assumes no prior knowledge in this area and leads up to cutting-edge research on sharp constants in LiebThirring inequalities.
'In 1975, Lieb and Thirring proved a remarkable bound of the sum of the negative eigenvalues of a Schrödinger operator in three dimensions in terms of the L^{5/2}-norm of the potential and used it in their proof of the stability of matterShortly thereafter, they realized it was a case of a lovely set of inequalities which generalize Sobolev inequalities and have come to be called Lieb-Thirring bounds. This has spawned an industry with literally hundreds of papers on extensions, generalizations and optimal constants. It is wonderful to have the literature presented and synthesized by three experts who begin by giving the background necessary for this book to be useful not only to specialists but to the novice wishing to understand a deep chapter in mathematical analysis.' Barry Simon, California Institute of Technology
'In a difficult 1968 paper Dyson and Lenard succeeded in proving the 'Stability of Matter' in quantum mechanics. In 1975 a much simpler proof was developed by Thirring and me with a new, multi-function, Sobolev like inequality, as well as a bound on the negative spectrum of Schrödinger operators. These and other bounds have become an important and useful branch of functional analysis and differential equations generally and quantum mechanics in particular. This book, written by three of the leading contributors to the area, carefully lays out the entire subject in a highly readable, yet complete description of these inequalities. They also give gently, yet thoroughly, all the necessary spectral theory and Sobolev theory background that a beginning student might need.' Elliott Lieb, Princeton University
'In a difficult 1968 paper Dyson and Lenard succeeded in proving the 'Stability of Matter' in quantum mechanics. In 1975 a much simpler proof was developed by Thirring and me with a new, multi-function, Sobolev like inequality, as well as a bound on the negative spectrum of Schrödinger operators. These and other bounds have become an important and useful branch of functional analysis and differential equations generally and quantum mechanics in particular. This book, written by three of the leading contributors to the area, carefully lays out the entire subject in a highly readable, yet complete description of these inequalities. They also give gently, yet thoroughly, all the necessary spectral theory and Sobolev theory background that a beginning student might need.' Elliott Lieb, Princeton University
Rupert L. Frank holds a chair in applied mathematics at LMU Munich and is doing research primarily in analysis and mathematical physics. He is an invited speaker at the 2022 International Congress of Mathematics. Ari Laptev is Professor at Imperial College London. His research interests include different aspects of spectral theory and functional inequalities. He is a member of the Royal Swedish Academy of Science, a Fellow of EurASc and a member of Academia Europaea. Timo Weidl is Professor at the University of Stuttgart. He works on spectral theory and mathematical physics.
| SKU | Nicht verfügbar |
| ISBN 13 | 9781009218467 |
| ISBN 10 | 1009218468 |
| Titel | Schrodinger Operators: Eigenvalues and LiebThirring Inequalities |
| Autor | Rupert L Frank |
| Serie | Cambridge Studies In Advanced Mathematics |
| Buchzustand | Nicht verfügbar |
| Bindungsart | Hardback |
| Verlag | Cambridge University Press |
| Erscheinungsjahr | 2022-11-17 |
| Seitenanzahl | 512 |
| Hinweis auf dem Einband | Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden. |
| Hinweis | Nicht verfügbar |