Details
| Original language | English |
|---|---|
| Pages (from-to) | 1187-1209 |
| Number of pages | 23 |
| Journal | International Journal of Phytoremediation |
| Volume | 83 |
| Issue number | 12 |
| Publication status | Published - Dec 2004 |
| Externally published | Yes |
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.
Keywords
- 41A65, 42C40, AMS Subject Classifications: 46E35, Approximation spaces, Besov spaces, Distributions, Interpolation spaces, Moduli of smoothness, Sobolev spaces, Wavelets
ASJC Scopus subject areas
- Environmental Science(all)
- Environmental Chemistry
- Environmental Science(all)
- Pollution
- Agricultural and Biological Sciences(all)
- Plant Science
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: International Journal of Phytoremediation, Vol. 83, No. 12, 12.2004, p. 1187-1209.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Wavelet decompositions of L 2 -functionals
AU - Haf, H.
AU - Hochmuth, R.
PY - 2004/12
Y1 - 2004/12
N2 - 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.
AB - 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.
KW - 41A65
KW - 42C40
KW - AMS Subject Classifications: 46E35
KW - Approximation spaces
KW - Besov spaces
KW - Distributions
KW - Interpolation spaces
KW - Moduli of smoothness
KW - Sobolev spaces
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=85064784969&partnerID=8YFLogxK
U2 - 10.1080/00036810410001724698
DO - 10.1080/00036810410001724698
M3 - Article
AN - SCOPUS:85064784969
VL - 83
SP - 1187
EP - 1209
JO - International Journal of Phytoremediation
JF - International Journal of Phytoremediation
SN - 1522-6514
IS - 12
ER -