Non-negative operators in Krein Spaces and rank one perturbations
Seiten
2016
TU Ilmenau Universitätsbibliothek (Verlag)
978-3-86360-141-6 (ISBN)
TU Ilmenau Universitätsbibliothek (Verlag)
978-3-86360-141-6 (ISBN)
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The presented thesis addresses problems in perturbation theory of operators in Krein spaces and is settled in the area of functional analysis.
We study the spectrum of a non-negative operator A in a Krein space (K, [·, ·]) under rank one perturbations in resolvent sense. The following two questions are answered:
(i) How does the spectral multiplicity in a gap of the essential spectrum of A change under rank one perturbations?
(ii) How does the Jordan structure at isolated eigenvalues of A change under rank one perturbations? More precisely, how does the number and the length of Jordan chains of A at a given eigenvalue change under a rank one perturbation?
To show these results we use amongst others boundary triplets for symmetric operators in Krein spaces and associated Weyl functions, realisations of generalized Nevanlinna-, D0-, and D1-functions, and algebraic properties of Krein spaces.
We study the spectrum of a non-negative operator A in a Krein space (K, [·, ·]) under rank one perturbations in resolvent sense. The following two questions are answered:
(i) How does the spectral multiplicity in a gap of the essential spectrum of A change under rank one perturbations?
(ii) How does the Jordan structure at isolated eigenvalues of A change under rank one perturbations? More precisely, how does the number and the length of Jordan chains of A at a given eigenvalue change under a rank one perturbation?
To show these results we use amongst others boundary triplets for symmetric operators in Krein spaces and associated Weyl functions, realisations of generalized Nevanlinna-, D0-, and D1-functions, and algebraic properties of Krein spaces.
| Erscheinungsdatum | 19.08.2016 |
|---|---|
| Verlagsort | Ilmenau |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Gewicht | 250 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Krein-Raum • Nichtnegativer Operator • Störungstheorie |
| ISBN-10 | 3-86360-141-6 / 3863601416 |
| ISBN-13 | 978-3-86360-141-6 / 9783863601416 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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