1.

Record Nr.

UNINA9910827525903321

Autore

Haslinger Friedrich

Titolo

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

Pubbl/distr/stampa

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

©2014

ISBN

3-11-037783-7

3-11-031535-1

Descrizione fisica

1 online resource (254 p.)

Collana

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

Classificazione

SK 620

Disciplina

515/.9

Soggetti

Neumann problem

Schrödinger operator

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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

Sommario/riassunto

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.