Wavelets and Besov spaces on Mauldin-Williams fractals.

Mats Bodin

doi:rae/1184700041

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Home > Journals > Real Anal. Exchange > Volume 32 > Issue 1 > Article

2006/2007 Wavelets and Besov spaces on Mauldin-Williams fractals.

Mats Bodin

Author Affiliations +

Mats Bodin¹
¹Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden

Real Anal. Exchange 32(1): 119-144 (2006/2007).

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Abstract

A. Jonsson has constructed wavelets of higher order on self-similar sets, and characterized Besov spaces on totally disconnected self-similar sets, by means of the magnitude of the coefficients in the wavelet expansion of the function. For a class of self-similar sets, W. Jin shows that such wavelets can be constructed by recursively calculating moments. We extend their results to a class of graph-directed self-similar sets, introduced by R. D. Mauldin and S. C. Williams.