Wavelet decompositions of L 2 -functionals
- authored by
- H. Haf, R. Hochmuth
- Abstract
Based on distribution-theoretical definitions of L 2 and Sobolev spaces given by Werner in [P. Werner (1970). A distribution-theoretical approach to certain Lebesgue and Sobolev spaces. J. Math. Anal. Appl., 29, 19–78.] real interpolation, Besov type spaces and approximation spaces with respect to multiresolution approximations are considered. The key for the investigation are generalized moduli of smoothness introduced by Haf in [H. Haf (1992). On the approximation of functionals in Sobolev spaces by singular integrals. Applicable Analysis, 45, 295–308.]. Those moduli of smoothness allow to connect the concept of L 2 -functionals with more recent developments in multiscale analysis, see e.g. [W. Dahmen (1995). Multiscale analysis, approximation, and interpolation spaces. In: C.K. Chui and L.L. Schumaker (Eds.), Approximation Theory VIII, Vol. 2: Wavelets and Multilevel Approximation, pp. 47–88.]. In particular, we derive wavelet characterizations for the Sobolev spaces introduced by Werner and establish stable wavelet decompositions of L 2 -functionals. Generalizations to more general spaces of functionals and applications are also mentioned.
- External Organisation(s)
-
University of Kassel
TU Bergakademie Freiberg - University of Resources
- Type
- Article
- Journal
- International Journal of Phytoremediation
- Volume
- 83
- Pages
- 1187-1209
- No. of pages
- 23
- ISSN
- 1522-6514
- Publication date
- 12.2004
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Environmental Chemistry, Pollution, Plant Science
- Electronic version(s)
-
https://doi.org/10.1080/00036810410001724698 (Access:
Unknown)
-
Details in the research portal "Research@Leibniz University"
