Asymptotic behavior of Fourier transforms of self-similar measures

Author:
Tian-You Hu

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1713-1720

MSC (2000):
Primary 42A38; Secondary 28A80.

Published electronically:
November 3, 2000

MathSciNet review:
1814101

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Let be a self-similar probability measure on satisfying where and Let be the Fourier transform of A necessary and sufficient condition for to approach zero at infinity is given. In particular, if and for then if and only if is a PV-number and is not a factor of . This generalizes the corresponding theorem of Erdös and Salem for the case

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Additional Information

**Tian-You Hu**

Affiliation:
Department of Mathematics, University of Wisconsin-Green Bay, Green Bay, Wisconsin 54311

Email:
hut@uwgb.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05709-9

Keywords:
Fourier transform,
PV-number,
self-similar measure

Received by editor(s):
August 6, 1999

Received by editor(s) in revised form:
September 16, 1999

Published electronically:
November 3, 2000

Communicated by:
Christopher D. Sogge

Article copyright:
© Copyright 2000
American Mathematical Society