Schrödinger operators : Eigenvalues and Lieb-Thirring inequalities / Rupert L. Frank, Ari Laptev, Timo Weidl.

Format:

Book

Author/Creator:

Frank, Rupert L., author.

Laptev, Ari, author.

Weidl, Timo, author.

Series:

Cambridge studies in advanced mathematics ; 200.

Cambridge studies in advanced mathematics ; 200

Language:

English

Subjects (All):

Schrödinger operator.

Physical Description:

1 online resource (xiii, 507 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge : Cambridge University Press, 2023.

Summary:

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.

Contents:

Overview

Part One. Background Material

1. Elements of operator theory

2. Elements of Sobolev space theory

Part Two. The Laplace and Schroedinger Operators

3. The Laplacian on a domain

4. The Schroedinger operator

Part Three. 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.

Notes:

Title from publisher's bibliographic system (viewed on 07 Nov 2022).

Includes bibliographical references and index.

ISBN:

9781009218443

1009218441

9781009218436

1009218433

OCLC:

1351519592