Commuting Nonselfadjoint Operators in Hilbert Space : Two Independent Studies
Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator f...
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Serie: | Lecture notes in mathematics
1272 |
| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Commuting nonselfadjoint operators in Hilbert space, two independent studies, Moshe S. Livšic, Leonid L. Waksman, 1987, Berlin, Springer-Verlag, 1 volume (114 pages), Lecture notes in mathematics, 3-540-18316-7 • Commuting Nonselfadjoint Operators in Hilbert Space, Texte imprimé, 9783662163139 |
| Riassunto: | Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves. |
|---|---|
| Descrizione del documento: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783540478775 (PDF) |
| ISSN: | 1617-9692 |
| Accesso: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |