Hjem

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.