The D-bar Neumann problem and Schrödinger operators / Friedrich Haslinger.

Format:

Book

Author/Creator:

Haslinger, Friedrich, author.

Series:

De Gruyter expositions in mathematics ; Volume 59.

De Gruyter Expositions in Mathematics, 0938-6572 ; Volume 59

Language:

English

German

Subjects (All):

Neumann problem.

Schrödinger operator.

Physical Description:

1 online resource (254 p.)

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2014.

Language Note:

German

Summary:

The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted to Bergman spaces of holomorphic d-bar functions in one and several complex variables. These operators are Hankel operators of special type. In the following the general complex is investigated on d-bar spaces over bounded pseudoconvex domains and on weighted d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator. The last part contains a detailed account of the application of the methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.

Contents:

Front matter

Preface

Contents

1. Bergman spaces

2. The canonical solution operator to

3. Spectral properties of the canonical solution operator to

4. The complex

5. Density of smooth forms

6. The weighted complex

7. The twisted complex

8. Applications

9. Spectral analysis

10. Schrödinger operators and Witten-Laplacians

11. Compactness

12. The Neumann operator and the Bergman projection

13. Compact resolvents

14. Spectrum of on the Fock space

15. Obstructions to compactness

Bibliography

Index

Backmatter

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

3-11-037783-7

3-11-031535-1

OCLC:

890071094