Non-self-adjoint differential operators, spectral asymptotics and random perturbations. ([2019])
- Record Type:
- Book
- Title:
- Non-self-adjoint differential operators, spectral asymptotics and random perturbations. ([2019])
- Main Title:
- Non-self-adjoint differential operators, spectral asymptotics and random perturbations
- Further Information:
- Note: Johannes Sjöstrand.
- Authors:
- Sjöstrand, J (Johannes)
- Contents:
- Intro; Abstract; Contents; 1 Introduction; Part I Basic Notions, Differential Operators in One Dimension; 2 Spectrum and Pseudo-Spectrum; 2.1 Operators in Hilbert Spaces, a Quick Review; 2.2 Pseudospectrum; 2.3 Numerical Range; 2.4 A Simple Example of a Large Matrix; 2.5 The Non-self-adjoint Harmonic Oscillator; 3 Weyl Asymptotics and Random Perturbations in a One-Dimensional Semi-classical Case; 3.1 Preparations for the Unperturbed Operator; 3.2 Grushin (Schur, Feschbach, Bifurcation) Approach; 3.3 d-Bar Equation for E-+; 3.4 Adding the Random Perturbation 4 Quasi-Modes and Spectral Instability in One Dimension4.1 Asymptotic WKB Solutions; 4.2 Quasimodes in One Dimension; 5 Spectral Asymptotics for More General Operators in One Dimension; 5.1 Preliminaries for the Unperturbed Operator; 5.2 The Result; 5.3 Preparations for the Unperturbed Operator; 5.4 d-Bar Equation for E-+; 5.5 Adding the Random Perturbation; 5.A Appendix: Estimates on Determinants of Gaussian Random Matrices; 6 Resolvent Estimates Near the Boundary of the Range of the Symbol; 6.1 Introduction and Statement of the Main Result; 6.2 Preparations and Reductions 13.5 Upper Bounds on the Number of Eigenvalues in the Interior13.6 Gaussian Elimination and Determinants; 13.7 Random Perturbations and Determinants; 13.8 Eigenvalue Distribution for Small Random Perturbations; 13.9 Eigenvalue Distribution for Larger Random Perturbations; Part III Spectral Asymptotics for Differential Operators in Higher Dimension; 14Intro; Abstract; Contents; 1 Introduction; Part I Basic Notions, Differential Operators in One Dimension; 2 Spectrum and Pseudo-Spectrum; 2.1 Operators in Hilbert Spaces, a Quick Review; 2.2 Pseudospectrum; 2.3 Numerical Range; 2.4 A Simple Example of a Large Matrix; 2.5 The Non-self-adjoint Harmonic Oscillator; 3 Weyl Asymptotics and Random Perturbations in a One-Dimensional Semi-classical Case; 3.1 Preparations for the Unperturbed Operator; 3.2 Grushin (Schur, Feschbach, Bifurcation) Approach; 3.3 d-Bar Equation for E-+; 3.4 Adding the Random Perturbation 4 Quasi-Modes and Spectral Instability in One Dimension4.1 Asymptotic WKB Solutions; 4.2 Quasimodes in One Dimension; 5 Spectral Asymptotics for More General Operators in One Dimension; 5.1 Preliminaries for the Unperturbed Operator; 5.2 The Result; 5.3 Preparations for the Unperturbed Operator; 5.4 d-Bar Equation for E-+; 5.5 Adding the Random Perturbation; 5.A Appendix: Estimates on Determinants of Gaussian Random Matrices; 6 Resolvent Estimates Near the Boundary of the Range of the Symbol; 6.1 Introduction and Statement of the Main Result; 6.2 Preparations and Reductions 13.5 Upper Bounds on the Number of Eigenvalues in the Interior13.6 Gaussian Elimination and Determinants; 13.7 Random Perturbations and Determinants; 13.8 Eigenvalue Distribution for Small Random Perturbations; 13.9 Eigenvalue Distribution for Larger Random Perturbations; Part III Spectral Asymptotics for Differential Operators in Higher Dimension; 14 Weyl Asymptotics for the Damped Wave Equation; 14.1 Eigenvalues of Perturbations of Self-adjoint Operators; 14.2 The Damped Wave Equation … (more)
- Publisher Details:
- Cham : Birkhäuser
- Publication Date:
- 2019
- Copyright Date:
- 2019
- Extent:
- 1 online resource, color illustrations
- Subjects:
- 515/.7246
Nonselfadjoint operators
Spectral theory (Mathematics)
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9783030108199
3030108198 - Related ISBNs:
- 9783030108182
- Notes:
- Note: Includes bibliographical references.
Note: Online resource ; title from PDF title page (EBSCO, viewed May 22, 2019). - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.425936
- Ingest File:
- 02_538.xml