Perturbation Theory for Linear Operators

2. Auflage 1995
ISBN: 978-3-540-58661-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 623 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1990 g

Reihe: Classics in Mathematics

From the reviews: "[…] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory. […] I can recommend it for any mathematician or physicist interested in this field." Zentralblatt MATH

Zielgruppe

Research

Autoren/Hrsg.

Kato, Tosio

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.

Über Autor(innen)

Biography of Tosio Kato

Tosio Kato was born in 1917 in a village to the north of Tokyo. He studied theoretical physics at the Imperial University of Tokyo. After several years of inactivity during World War II due to poor health, he joined the Faculty of Science at the University of Tokyo in 1951. From 1962 he was Professor of Mathematics at the University of California, Berkeley, where he is now Professor Emeritus.

Kato was a pioneer in modern mathematical physics. He worked in te areas of operator theory, quantum mechanics, hydrodynamics, and partial differential equations, both linear and nonlinear.