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John W.G. Cairney: Partial Differential Equations VII : Spectral Theory of Differential Operators
- neues Buch ISBN: 9783662067192
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General … Mehr…
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrodinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20. 5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me- chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera- tor.In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series.; PDF; Scientific, Technical and Medical > Mathematics > Calculus & mathematical analysis, Springer Berlin Heidelberg<
hive.co.uk No. 9783662067192. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
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Pierre Meystre: Partial Differential Equations VII : Spectral Theory of Differential Operators
- neues Buch ISBN: 9783662067192
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General … Mehr…
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrodinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20. 5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me- chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera- tor.In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series.; PDF; Scientific, Technical and Medical > Mathematics > Calculus & mathematical analysis, Springer Berlin Heidelberg<
hive.co.uk No. 9783662067192. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
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V.I. Arnol'd: Partial Differential Equations VII : Spectral Theory of Differential Operators
- neues Buch ISBN: 9783662067192
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General … Mehr…
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrodinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20. 5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me- chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera- tor.In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series.; PDF; Scientific, Technical and Medical > Mathematics > Calculus & mathematical analysis, Springer Berlin Heidelberg<
hive.co.uk No. 9783662067192. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
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Partial Differential Equations VII
- neues Buch ISBN: 9783662067192
§18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General… Mehr…
§18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrödinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 §19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 §20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20. 5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera tor. In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series., Springer<
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A. Schutz: Partial Differential Equations VII : Spectral Theory of Differential Operators
- neues Buch ISBN: 9783662067192
; PDF; Scientific, Technical and Medical > Mathematics > Calculus & mathematical analysis, Springer Netherlands
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John W.G. Cairney: Partial Differential Equations VII : Spectral Theory of Differential Operators - neues Buch ISBN: 9783662067192
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General … Mehr…
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrodinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20. 5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me- chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera- tor.In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series.; PDF; Scientific, Technical and Medical > Mathematics > Calculus & mathematical analysis, Springer Berlin Heidelberg<
No. 9783662067192. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
2
Pierre Meystre: Partial Differential Equations VII : Spectral Theory of Differential Operators
- neues Buch ISBN: 9783662067192
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General … Mehr…
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrodinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20. 5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me- chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera- tor.In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series.; PDF; Scientific, Technical and Medical > Mathematics > Calculus & mathematical analysis, Springer Berlin Heidelberg<
No. 9783662067192. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
3
V.I. Arnol'd: Partial Differential Equations VII : Spectral Theory of Differential Operators
- neues Buch 18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General … Mehr…
18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrodinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20. 5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me- chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera- tor.In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series.; PDF; Scientific, Technical and Medical > Mathematics > Calculus & mathematical analysis, Springer Berlin Heidelberg<
No. 9783662067192. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
4
Partial Differential Equations VII
- neues Buch ISBN: 9783662067192
§18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General… Mehr…
§18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrödinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 §19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 §20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20. 5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera tor. In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series., Springer<
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A. Schutz: Partial Differential Equations VII : Spectral Theory of Differential Operators
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Detailangaben zum Buch - Partial Differential Equations VII
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Daten vom Verlag: Autor/in: M.A. Shubin
EA; E107; eBook; Nonbooks, PBS / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Eigenvalue; Perturbation of Eigenvalues; Spectral Asymptotics; Spectral Geometry; Spektralasymptotik; Spektralgeometrie; Spektren von Differentialoperatoren; differential equation; operator; partial differential equation; spectra of differential operators; A; Analysis; Theoretical, Mathematical and Computational Physics; Differential Geometry; Mathematical Applications in Chemistry; Computational Intelligence; Mathematics and Statistics; Mathematische Physik; Differentielle und Riemannsche Geometrie; Quanten- und theoretische Chemie; Künstliche Intelligenz; BB
Contents: Spectral Theory of Differential Operators by G.V. Rozenblum, M.A. Shubin, M.Z. Solomyak.
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Special attention is devoted to the operators of mathematical physics. The book will be used by graduate students and researchers in mathematics and physics and also by engineers interested in partial differential equations.
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