Author | Kato, Tosio. author |
---|---|
Title | Perturbation Theory for Linear Operators [electronic resource] / by Tosio Kato |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1976 |
Edition | Corrected Printing of the Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-66282-9 |
Descript | XXI, 623 p. online resource |
One Operator theory in finite-dimensional vector spaces -- ยง 1. Vector spaces and normed vector spaces -- ยง 2. Linear forms and the adjoint space -- ยง 3. Linear operators -- ยง 4. Analysis with operators -- ยง 5. The eigenvalue problem -- ยง 6. Operators in unitary spaces -- Two Perturbation theory in a finite-dimensional space -- ยง 1. Analytic perturbation of eigenvalues -- ยง 2. Perturbation series -- ยง 3. Convergence radii and error estimates -- ยง . Similarity transformations of the eigenspaces and eigenvectors -- ยง 5. Non-analytic perturbations -- ยง 6. Perturbation of symmetric operators -- Three Introduction to the theory of operators in Banach spaces -- ยง 1. Banach spaces -- ยง 2. Linear operators in Banach spaces -- ยง 3. Bounded operators -- ยง 4. Compact operators -- ยง 5. Closed operators -- ยง 6. Resolvents and spectra -- Four Stability theorems -- ยง1. Stability of closedness and bounded invertibility -- ยง 2. Generalized convergence of closed operators -- ยง 3. Perturbation of the spectrum -- ยง 4. Pairs of closed linear manifolds -- ยง 5. Stability theorems for semi-Fredholm operators -- ยง 6. Degenerate perturbations -- Five Operators in Hilbert spaces -- ยง 1. Hilbert space -- ยง 2. Bounded operators in Hilbert spaces -- ยง 3. Unbounded operators in Hilbert spaces -- ยง 4. Perturbation of self adjoint operators -- ยง 5. The Schrรถdinger and Dirac operators -- Six Sesquilinear forms in Hilbert spaces and associated operators -- ยง 1. Sesquilinear and quadratic forms -- ยง 2. The representation theorems -- ยง 3. Perturbation of sesquilinear forms and the associated operators -- ยง 4. Quadratic forms and the Schrรถdinger operators -- ยง 5. The spectral theorem and perturbation of spectral families -- Seven Analytic perturbation theory -- ยง 1. Analytic families of operators -- ยง 2. Holomorphic families of type (A) -- ยง 3. Selfadjoint holomorphic families -- ยง 4. Holomorphic families of type (B) -- ยง 5. Further problems of analytic perturbation theory -- ยง 6. Eigenvalue problems in the generalized form -- Eight Asymptotic perturbation theory -- ยง 1. Strong convergence in the generalized sense -- ยง 2. Asymptotic expansions -- ยง 3. Generalized strong convergence of sectorial operators -- ยง 4. Asymptotic expansions for sectorial operators -- ยง 5. Spectral concentration -- Nine Perturbation theory for semigroups of operators -- ยง 1. One-parameter semigroups and groups of operators -- ยง 2. Perturbation of semigroups -- ยง 3. Approximation by discrete semigroups -- Ten Perturbation of continuous spectra and unitary equivalence -- ยง1. The continuous spectrum of a selfadjoint operator -- ยง 2. Perturbation of continuous spectra -- ยง 3. Wave operators and the stability of absolutely continuous spectra -- ยง 4. Existence and completeness of wave operators -- ยง 5. A stationary method -- Supplementary Notes -- Supplementary Bibliography -- Notation index -- Author index