
Open access
Datum
2004-07Typ
- Journal Article
Abstract
We establish multiresolution norm equivalences in weighted spaces $L^2_w$ ((0,1)) with possibly singular weight functions $w(x) \geq 0$ 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 $w(x)$ 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 $p$-Version FEM and wavelet discretizations of degenerate elliptic and parabolic problems from finance. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-b-000049976Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
Numerische MathematikBand
Seiten / Artikelnummer
Verlag
SpringerOrganisationseinheit
03435 - Schwab, Christoph / Schwab, Christoph
Anmerkungen
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher