with the publication of volumes iii and iv we have completed our presentation of the material which we originally planned as "volume ii" at the time of publication of volume i. we originally promised the publisher that the entire series would be completed nine months after we submitted volume i. well! we have listed the contents of future volumes below. we are not foolhardy enough to make any predictions.
目录
Preface Introduction Contents of Other Volumes XII: PERTURBATION OF POINT SPECTRA 1. Finite-dimensional perturbation theory Appendix Algebraic and geometric multiplicity of eigenvalues of finite matrices 2. Regular perturbation theory 3. Asymptotic perturbation theory 4. Summability methods in perturbation theory 5. Spectral concentration 6. Resonances and the Fermi golden rule Notes Problems XlII: SPECTRAL ANALYSIS 1. The rain-max principle 2. Bound states of Schr‘6dinger operators I: Quantitative methods 3. Bound states of Schr‘odinger operators II: Qualitative theory A. Is disc (H)finite or infinite? B. Bounds on N(V) in the central case C. Bounds on N(V) in the general two-body case 4. Locating the essential spectrum I: Weyl's theorem 5. Locating the essential spectrum III: Tire HVZ theorem 6. The absence of singular continuous spectrum I: General theory 7. The absence of singular continuous spectrum II: Smooth perturbations A. Weakly coupled quantum systems B. Positive commutators and repulsive potentials C. Local smoothness and wave operators for repulsive potentials 8. The absence of singular continuous spectrum III: Weighted L2 spaces 9. The spectrum ofctensor products 10.The absence of singular continuous spectrum IV: Dilation analytic potentials 11. Properties of eigenfitnctions 12. Nondegeneracy of the ground state Appendix 1 The Beurling-Deny criteria Appendix 2 The Levy-Khintchinecformula 13. Absence of positive eigenvalues Appendix Unique continuation theorems for Schrodinger operators 14. Compactness criteria and operators with compact resolvent 15. The asymptotic distribution of eigenvalues 16. Schr6dinger operators with periodic potentials 17. An introduction to the specral theory of non-self-adjoint operators Notes Problems List of Symbols Index
