Self-similar measures and their Fourier transforms. II

Author:
Robert S. Strichartz

Journal:
Trans. Amer. Math. Soc. **336** (1993), 335-361

MSC:
Primary 42B10

DOI:
https://doi.org/10.1090/S0002-9947-1993-1081941-2

MathSciNet review:
1081941

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Abstract: A self-similar measure on was defined by Hutchinson to be a probability measure satisfying

*self-similar distribution*by the same identity but allowing the weights to be arbitrary complex numbers. We give necessary and sufficient conditions for the existence of a solution to among distributions of compact support, and show that the space of such solutions is always finite dimensional.

If denotes the Fourier transformation of a self-similar distribution of compact support, let

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DOI:
https://doi.org/10.1090/S0002-9947-1993-1081941-2

Article copyright:
© Copyright 1993
American Mathematical Society