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Random  -adic Riesz products: Continuity, singularity, and dimension
Author(s):
Narn-Rueih
Shieh;
Xiong-ying
Zhang
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3477-3486.
MSC (2000):
Primary 60G57, 28A80, 11S80
Posted:
June 3, 2009
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Additional information
Abstract:
We study precise conditions for mutual absolute continuity and mutual singularity of two random  -adic Riesz products, defined respectively by two sequences of coefficients  . Our conditions and assertions are specific to the  -adic case. We also calculate explicitly the Hausdorff dimension, and in case the defining coefficients are constant, we have an integral representation of the dimension formula with a rapid convergence rate  .
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Additional Information:
Narn-Rueih
Shieh
Affiliation:
Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan
Email:
shiehnr@math.ntu.edu.tw
Xiong-ying
Zhang
Affiliation:
Department of Mathematics, South China University of Technology, 510640 Guangzhou, People's Republic of China
Email:
xiongyzh@scut.edu.cn
DOI:
10.1090/S0002-9939-09-09991-2
PII:
S 0002-9939(09)09991-2
Keywords:
Random $p$-adic Riesz products,
mutual absolute continuity,
mutual singularity,
Hausdorff dimension
Received by editor(s):
June 9, 2008
Posted:
June 3, 2009
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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