Spectral Theory of Ordinary Differential Operators
These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating...
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| Главный автор: | |
|---|---|
| Формат: | Livre numérique |
| Язык: | Anglais |
| Опубликовано: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Серии: | Lecture notes in mathematics
1258 |
| Предметы: | |
| Online-ссылка: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Примечание: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Spectral theory of ordinary differential operators, Joachim Weidmann, 1987, Berlin, Springer-Verlag, 1 volume (VI-303 pages), Lecture notes in mathematics, 978-3-540-17902-3 • Spectral Theory of Ordinary Differential Operators, Texte imprimé, 9783662188750 |
Оглавление:
- Formally self-adjoint differential expressions
- Appendix to section 1: The separation of the Dirac operator
- Fundamental properties and general assumptions
- Appendix to section 2: Proof of the Lagrange identity for n>2
- The minimal operator and the maximal operator
- Deficiency indices and self-adjoint extensions of T0
- The solutions of the inhomogeneous differential equation (?-?)u=f; Weyl's alternative
- Limit point-limit circle criteria
- Appendix to section 6: Semi-boundedness of Sturm-Liouville type operators
- The resolvents of self-adjoint extensions of T0
- The spectral representation of self-adjoint extensions of T0
- Computation of the spectral matrix ?
- Special properties of the spectral representation, spectral multiplicities
- L2-solutions and essential spectrum
- Differential operators with periodic coefficients
- Appendix to section 12: Operators with periodic coefficients on the half-line
- Oscillation theory for regular Sturm-Liouville operators
- Oscillation theory for singular Sturm-Liouville operators
- Essential spectrum and absolutely continuous spectrum of Sturm-Liouville operators
- Oscillation theory for Dirac systems, essential spectrum and absolutely continuous spectrum
- Some explicitly solvable problems.