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Haar wavelets of higher order on fractals and regularity of functions
Umeå University, Faculty of Science and Technology, Department of mathematics.
2004 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 290, no 1, 86-104 p.Article in journal (Refereed) Published
Abstract [en]

Wavelets of Haar type of higher order m on self-similar fractals were introduced by the author in J. Fourier Anal. Appl. 4 (1998) 329–340. These are piecewise polynomials of degree m instead of piecewise constants. It was shown that for certain totally disconnected fractals, spaces of functions defined on the fractal may be characterized by means of the magnitude of the wavelet coefficients of the functions. In this paper, the study of these wavelets is continued. It is shown that also in the case when the fractals are not totally disconnected, the wavelets can be used to study regularity properties of functions. In particular, the self-similar sets considered can be, e.g., an interval in R or a cube in Rn. It turns out that it is natural to use Haar wavelets of higher order also in these classical cases, and many of the results in the paper are new also for these sets.

Place, publisher, year, edition, pages
San Diego: Academic Press, 2004. Vol. 290, no 1, 86-104 p.
Keyword [en]
Wavelets, Function spaces, Fractals
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-19699DOI: 10.1016/j.jmaa.2003.09.071ISI: 000188777500008OAI: oai:DiVA.org:umu-19699DiVA: diva2:202374
Available from: 2009-03-10 Created: 2009-03-10 Last updated: 2017-12-13Bibliographically approved

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