- AutorIn
- Dr. Marko Lindner
- Titel
- Fredholm Theory and Stable Approximation of Band Operators and Their Generalisations
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:ch1-200901182
- Datum der Einreichung
- 23.02.2009
- Datum der Verteidigung
- 09.07.2009
- Abstract (EN)
- This text is concerned with the Fredholm theory and stable approximation of bounded linear operators generated by a class of infinite matrices $(a_{ij})$ that are either banded or have certain decay properties as one goes away from the main diagonal. The operators are studied on $\ell^p$ spaces of functions $\Z^N\to X$, where $p\in[1,\infty]$, $N\in\N$ and $X$ is a complex Banach space. The latter means that our matrix entries $a_{ij}$ are indexed by multiindices $i,j\in\Z^N$ and that every $a_{ij}$ is itself a bounded linear operator on $X$. Our main focus lies on the case $p=\infty$, where new results are derived, and it is demonstrated in both general theory and concrete operator equations from mathematical physics how advantage can be taken of these new $p=\infty$ results in the general case $p\in[1,\infty]$.
- Klassifikation (DDC)
- 500
- Normschlagwörter (GND)
- Fredholm-Operator
- Hamilton-Operator
- Integraloperator
- Spektraltheorie
- Zufallsoperator
- GutachterIn
- Prof. Dr. Albrecht Böttcher
- Prof. Dr. Hermann Schulz-Baldes
- Prof. Dr. Simon Chandler-Wilde
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Chemnitz, Chemnitz
- URN Qucosa
- urn:nbn:de:bsz:ch1-200901182
- Veröffentlichungsdatum Qucosa
- 23.07.2009
- Dokumenttyp
- Habilitation
- Sprache des Dokumentes
- Englisch