Perturbation Theory for Linear Operators (Classics in Mathematics, 132, Band 132) - Taschenbuch

EAN (ISBN-13): 9783540586616
ISBN (ISBN-10): 354058661X
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 1995
Herausgeber: Springer

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ISBN/EAN: 354058661X

ISBN - alternative Schreibweisen:
3-540-58661-X, 978-3-540-58661-6
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: tosio kato, tosi
Titel des Buches: linear theory, for operators, perturbation theory look chemical, operator theory, the, cycle classsic, classics mathematics, kato, perturbation short, 132

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Daten vom Verlag:

Autor/in: Tosio Kato
Titel: Classics in Mathematics; Perturbation Theory for Linear Operators
Verlag: Springer; Springer Berlin
623 Seiten
Erscheinungsjahr: 1995-02-15
Berlin; Heidelberg; DE
Sprache: Englisch
58,84 € (DE)
60,49 € (AT)
65,00 CHF (CH)
Available
XXI, 623 p.

BC; Hardcover, Softcover / Mathematik/Analysis; Differentialrechnung und -gleichungen; Verstehen; Excel; Hilbert space; Linear Operators; differential equation; differential operator; field; function; functional; functional analysis; perturbation; perturbation theory; review; ring theory; scattering theory; partial differential equations; Differential Equations; Calculus of Variations and Optimization; Optimierung; BB

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.