The d-bar Neumann Problem and Schrödinger Operators /
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 toBergman spaces of holomorphic d-bar functions in one and several complex variables.These operators...
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| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston :
De Gruyter,
[2014]
Berlin ; Boston : [2014] Berlin, [Germany] ; Boston, [Massachusetts] : 2014 |
| Series: | De Gruyter expositions in mathematics ;
Volume 59 De Gruyter expositions in mathematics 59 |
| Subjects: |
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| 100 | 1 | |a Haslinger, Friedrich, |e author | |
| 245 | 1 | 4 | |a The d-bar Neumann Problem and Schrödinger Operators / |c Friedrich Haslinger |
| 264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2014] | |
| 264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2014] | |
| 264 | 1 | |a Berlin, [Germany] ; |a Boston, [Massachusetts] : |b De Gruyter, |c 2014 | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (241 pages) | ||
| 300 | |a 1 online resource (252 p) | ||
| 300 | |a 1 online resource (254 pages) | ||
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| 490 | 0 | |a De Gruyter Expositions in Mathematics , |x 0938-6572 ; |v 59 | |
| 490 | 1 | |a De Gruyter Expositions in Mathematics ; |v 59 | |
| 490 | 1 | |a De Gruyter Expositions in Mathematics, |x 0938-6572 ; |v Volume 59 | |
| 504 | |a Includes bibliographical references and index | ||
| 505 | 0 | 0 | |t Frontmatter -- |t Preface -- |t Contents -- |t 1. Bergman spaces -- |t 2. The canonical solution operator to ∂̄ -- |t 3. Spectral properties of the canonical solution operator to ∂̄ -- |t 4. The ∂̄-complex -- |t 5. Density of smooth forms -- |t 6. The weighted ∂̄-complex -- |t 7. The twisted ∂̄-complex -- |t 8. Applications -- |t 9. Spectral analysis -- |t 10. Schrödinger operators and Witten-Laplacians -- |t 11. Compactness -- |t 12. The ∂̄-Neumann operator and the Bergman projection -- |t 13. Compact resolvents -- |t 14. Spectrum of ◻ on the Fock space -- |t 15. Obstructions to compactness -- |t Bibliography -- |t Index -- |t Backmatter |
| 505 | 0 | 0 | |t Frontmatter -- |t Preface -- |t Contents -- |t 1. Bergman spaces -- |t 2. The canonical solution operator to ∂̄ -- |t 3. Spectral properties of the canonical solution operator to ∂̄ -- |t 4. The ∂̄-complex -- |t 5. Density of smooth forms -- |t 6. The weighted ∂̄-complex -- |t 7. The twisted ∂̄-complex -- |t 8. Applications -- |t 9. Spectral analysis -- |t 10. Schrödinger operators and Witten-Laplacians -- |t 11. Compactness -- |t 12. The ∂̄-Neumann operator and the Bergman projection -- |t 13. Compact resolvents -- |t 14. Spectrum of ◻ on the Fock space -- |t 15. Obstructions to compactness -- |t Bibliography -- |t Index -- |t Backmatter |
| 506 | |a Access restricted by licensing agreement | ||
| 506 | |a Restricted for use by site license. | ||
| 520 | |a 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 toBergman 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 | ||
| 520 | |a 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 toBergman 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 | ||
| 530 | |a Issued also in printing | ||
| 538 | |a Mode of access: Internet via World Wide Web | ||
| 546 | |a In English | ||
| 588 | |a Description based on print version record | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 01. Dez 2022) | |
| 588 | 0 | |a Description based on online resource; title from PDF title page (publishers Web site, viewed 08. Jul 2019) | |
| 590 | |a Access is available to the Yale community | ||
| 596 | |a 22 | ||
| 650 | 0 | |a Neumann problem | |
| 650 | 0 | |a Schrödinger operator | |
| 650 | 0 | |a Schrödinger operator |= ^A1058778 | |
| 650 | 4 | |a Compactness | |
| 650 | 4 | |a Funktionentheorie | |
| 650 | 4 | |a Hankel Operator | |
| 650 | 4 | |a Inhomogeneous Cauchy-Riemann Equation | |
| 650 | 4 | |a Neumannproblem | |
| 650 | 4 | |a Schrödingeroperator | |
| 650 | 4 | |a Witten Laplacian | |
| 650 | 4 | |a d-bar Neumann Problem | |
| 650 | 7 | |0 (DE-601)105393894 |a Neumann-Problem |2 gnd | |
| 650 | 7 | |0 (DE-601)105576913 |a Cauchy-Riemannsche Differentialgleichungen |2 gnd | |
| 650 | 7 | |0 (DE-601)106095722 |a Hamilton-Operator |2 gnd | |
| 650 | 7 | |0 (DE-601)126498431 |a Hankel-Operator |2 gnd | |
| 650 | 7 | |0 (DE-601)229232760 |a Kompaktheit |2 gnd | |
| 650 | 7 | |a MATHEMATICS / General |2 bisacsh | |
| 653 | |a Compactness | ||
| 653 | |a Hankel Operator | ||
| 653 | |a Inhomogeneous Cauchy-Riemann Equation | ||
| 653 | |a Schrödinger Operator | ||
| 653 | |a Witten Laplacian | ||
| 653 | |a d-bar Neumann Problem | ||
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