Fredholm Theory and Stable Approximation of Band Operators and Their Generalisations
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 f...
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| Format: | Doctoral Thesis |
| Language: | English |
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Universitätsbibliothek Chemnitz
2009
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| Online Access: | http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901182 http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901182 http://www.qucosa.de/fileadmin/data/qucosa/documents/5840/data/Habil.pdf http://www.qucosa.de/fileadmin/data/qucosa/documents/5840/20090118.txt |
| Summary: | 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
$p\in[1,\infty]$. |
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