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Perturbation Theory for Linear Operators /
In view of recent development in perturbation theory, supplementary notes and a supplementary bibliography are added at the end of the new edition. Little change has been made in the text except that the paraƯ graphs V-ʹ 4.5, VI-ʹ 4.3, and VIII-ʹ 1.4 have been completely rewritten, and a number of m...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint : Springer,
1976.
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| Edición: | Corrected printing of the Second edition. |
| Colección: | Classics in mathematics,
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- One Operator theory in finite-dimensional vector spaces
- § 1. Vector spaces and normed vector spaces
- § 2. Linear forms and the adjoint space
- § 3. Linear operators
- § 4. Analysis with operators
- § 5. The eigenvalue problem
- § 6. Operators in unitary spaces
- Two Perturbation theory in a finite-dimensional space
- § 1. Analytic perturbation of eigenvalues
- § 2. Perturbation series
- § 3. Convergence radii and error estimates
- § . Similarity transformations of the eigenspaces and eigenvectors
- § 5. Non-analytic perturbations
- § 6. Perturbation of symmetric operators
- Three Introduction to the theory of operators in Banach spaces
- § 1. Banach spaces
- § 2. Linear operators in Banach spaces
- § 3. Bounded operators
- § 4. Compact operators
- § 5. Closed operators
- § 6. Resolvents and spectra
- Four Stability theorems
- §1. Stability of closedness and bounded invertibility
- § 2. Generalized convergence of closed operators
- § 3. Perturbation of the spectrum
- § 4. Pairs of closed linear manifolds
- § 5. Stability theorems for semi-Fredholm operators
- § 6. Degenerate perturbations
- Five Operators in Hilbert spaces
- § 1. Hilbert space
- § 2. Bounded operators in Hilbert spaces
- § 3. Unbounded operators in Hilbert spaces
- § 4. Perturbation of self adjoint operators
- § 5. The Schrödinger and Dirac operators
- Six Sesquilinear forms in Hilbert spaces and associated operators
- § 1. Sesquilinear and quadratic forms
- § 2. The representation theorems
- § 3. Perturbation of sesquilinear forms and the associated operators
- § 4. Quadratic forms and the Schrödinger operators
- § 5. The spectral theorem and perturbation of spectral families
- Seven Analytic perturbation theory
- § 1. Analytic families of operators
- § 2. Holomorphic families of type (A)
- § 3. Selfadjoint holomorphic families
- § 4. Holomorphic families of type (B)
- § 5. Further problems of analytic perturbation theory
- § 6. Eigenvalue problems in the generalized form
- Eight Asymptotic perturbation theory
- § 1. Strong convergence in the generalized sense
- § 2. Asymptotic expansions
- § 3. Generalized strong convergence of sectorial operators
- § 4. Asymptotic expansions for sectorial operators
- § 5. Spectral concentration
- Nine Perturbation theory for semigroups of operators
- § 1. One-parameter semigroups and groups of operators
- § 2. Perturbation of semigroups
- § 3. Approximation by discrete semigroups
- Ten Perturbation of continuous spectra and unitary equivalence
- §1. The continuous spectrum of a selfadjoint operator
- § 2. Perturbation of continuous spectra
- § 3. Wave operators and the stability of absolutely continuous spectra
- § 4. Existence and completeness of wave operators
- § 5. A stationary method
- Supplementary Notes
- Supplementary Bibliography
- Notation index
- Author index.