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Schrödinger Operators: Eigenvalues and Lieb-Thirring Inequalities
Buch von Rupert L Frank (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
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.
Inhaltsverzeichnis
Overview; Part I. Background Material: 1. Elements of operator theory; 2. Elements of Sobolev space theory; Part II. The Laplace and Schrödinger Operators: 3. The Laplacian on a domain; 4. The Schrödinger 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.
Details
Erscheinungsjahr: 2022
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 512
Inhalt: Gebunden
ISBN-13: 9781009218467
ISBN-10: 1009218468
Sprache: Englisch
Einband: Gebunden
Autor: Frank, Rupert L
Laptev, Ari
Weidl, Timo
Hersteller: European Community
Maße: 232 x 157 x 36 mm
Von/Mit: Rupert L Frank (u. a.)
Erscheinungsdatum: 17.11.2022
Gewicht: 0,846 kg
preigu-id: 122044134
Über den Autor
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.
Inhaltsverzeichnis
Overview; Part I. Background Material: 1. Elements of operator theory; 2. Elements of Sobolev space theory; Part II. The Laplace and Schrödinger Operators: 3. The Laplacian on a domain; 4. The Schrödinger 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.
Details
Erscheinungsjahr: 2022
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 512
Inhalt: Gebunden
ISBN-13: 9781009218467
ISBN-10: 1009218468
Sprache: Englisch
Einband: Gebunden
Autor: Frank, Rupert L
Laptev, Ari
Weidl, Timo
Hersteller: European Community
Maße: 232 x 157 x 36 mm
Von/Mit: Rupert L Frank (u. a.)
Erscheinungsdatum: 17.11.2022
Gewicht: 0,846 kg
preigu-id: 122044134
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