The local dimensions of the

Bernoulli convolution associated with

the golden number

Author:
Tian-You Hu

Journal:
Trans. Amer. Math. Soc. **349** (1997), 2917-2940

MSC (1991):
Primary 28A80; Secondary 42A85

DOI:
https://doi.org/10.1090/S0002-9947-97-01474-8

MathSciNet review:
1321578

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a sequence of i.i.d. random variables each taking values of 1 and with equal probability. For satisfying the equation , let be the probability measure induced by . For any in the range of , let

be the local dimension of at whenever the limit exists. We prove that

where , are respectively the maximum and minimum values of the local dimensions. If , then is the golden number, and the approximate numerical values are and .

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Additional Information

**Tian-You Hu**

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

Email:
HUT@gbms01.uwgb.edu

DOI:
https://doi.org/10.1090/S0002-9947-97-01474-8

Keywords:
Bernoulli convolution,
Fibonacci sequence,
local dimension,
PV-number

Received by editor(s):
August 23, 1994

Received by editor(s) in revised form:
January 25, 1995

Article copyright:
© Copyright 1997
American Mathematical Society