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Large-Scale Renormalisation of Fourier Transforms of Self-Similar Measures and Self-Similarity of Riesz Measures

✍ Scribed by Matthias Holschneider

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 128 KB
Volume: 200
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0206

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✦ Synopsis

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.

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