An Improved Multifractal Formalism and Self-Similar Measures
β Scribed by R. Riedi
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 959 KB
- Volume
- 189
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
We define the notion of quasi self-similar measures and show that for such measures their generalised Hausdorff and packing measures are positive and finite at the critical exponent. In practice this allows easy calculation of their dimension functions. We then show that a coarse form of the multifr
By then applying the definitions in (2.5), we get z=dim,, K=dim,? K=dim, K. (1.5) For Sierpinski carpets [18]. (1.5) does not hold. Furthermore, we give 143
## Abstract By now the multifractal structure of selfβsimilar measures satisfying the soβcalled Open Set Condition is well understood. However, if the Open Set Condition is not satisfied, then almost nothing is known. In this paper we prove a nontrivial lower bound for the symbolic multifractal spe
We shall show that the oscillations observed by R. S. Strichartz in the Fourier transforms of self-similar measures have a large-scale renormalisation given by a Riesz measure. Vice versa the Riesz measure itself will be shown to be self-similar around every triadic point.