We establish multiresolution norm equivalences in
weighted spaces <i>L<sup>2</sup><sub>w</sub></i>((0,1))
with possibly singular weight functions <i>w(x)</i>≥0
in (0,1).
Our analysis exploits the locality of the
biorthogonal wavelet basis and its dual basis
functions. The discrete norms are sums of wavelet
coefficients which are weighted with respect to the
collocated weight function <i>w(x)</i> within each scale.
Since norm equivalences for Sobolev norms are by now
well-known, our result can also be applied to
weighted Sobolev norms. We apply our theory to
the problem of preconditioning <i>p</i>-Version FEM
and wavelet discretizations of degenerate
elliptic problems.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200600503 |
| Date | 05 April 2006 |
| Creators | Beuchler, Sven, Schneider, Reinhold, Schwab, Christoph |
| Contributors | TU Chemnitz, SFB 393 |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | text/html, text/plain, image/png, image/gif, text/plain, image/gif, application/pdf, application/x-gzip, text/plain, application/zip |
| Source | Preprintreihe des Chemnitzer SFB 393, 02-09 |
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