Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Multiresolution weighted norm equivalences and applications

by S. Beuchler and R. Schneider and Ch. Schwab

(Report number 2002-13)

Abstract
We establish multiresolution norm equivalences in weighted spaces L2w((0,1)) with possibly singular weight functions w(x) >= 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 problems.

Keywords:

@Techreport{BSS02_299,
  author = {S. Beuchler and R. Schneider and Ch. Schwab},
  title = {Multiresolution weighted norm equivalences and applications},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-13},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-13.pdf },
  year = {2002}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).