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.

Spectral theory (Mathematics).

Sobolev spaces.

Physical Description:

xiii, 507 pages : illustrations ; 24 cm.

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."- publisher

Contents:

Part I. Background Material:

Elements of operator theory

Elements of Sobolev space theory

Part II. The Laplace and Schrödinger Operators:

The Laplacian on a domain

The Schrödinger operator

Part III. Sharp Constants in Lieb-Thirring Inequalities:

Sharp Lieb-Thirring inequalities

Sharp Lieb-Thirring inequalities in higher dimensions

More on sharp Lieb-Thirring inequalities

More on the Lieb-Thirring constants.

Notes:

Includes bibliographical references and index.

ISBN:

9781009218467

1009218468

OCLC:

1338666011