Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1187-1209 |
| Seitenumfang | 23 |
| Fachzeitschrift | International Journal of Phytoremediation |
| Jahrgang | 83 |
| Ausgabenummer | 12 |
| Publikationsstatus | Veröffentlicht - Dez. 2004 |
| Extern publiziert | Ja |
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.
ASJC Scopus Sachgebiete
- Umweltwissenschaften (insg.)
- Umweltchemie
- Umweltwissenschaften (insg.)
- Umweltverschmutzung
- Agrar- und Biowissenschaften (insg.)
- Pflanzenkunde
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: International Journal of Phytoremediation, Jahrgang 83, Nr. 12, 12.2004, S. 1187-1209.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -