LARGE-SCALE RENORMALISATION OF FOURIER TRANSFORMS OF SELF-SIMILAR MEASURES AND SELF-SIMILARITY OF RIESZ MEASURES

摘要

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. (C) 1996 Academic Press, Inc. [References: 5]