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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Random $p$-adic Riesz products: Continuity, singularity, and dimension
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by Narn-Rueih Shieh and Xiong-ying Zhang PDF
Proc. Amer. Math. Soc. 137 (2009), 3477-3486 Request permission

Abstract:

We study precise conditions for mutual absolute continuity and mutual singularity of two random $p$-adic Riesz products, defined respectively by two sequences of coefficients $a_k, b_k$. Our conditions and assertions are specific to the $p$-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 $p^{-k}$.
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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
  • Received by editor(s): June 9, 2008
  • Published electronically: June 3, 2009
  • Communicated by: Richard C. Bradley
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 3477-3486
  • MSC (2000): Primary 60G57, 28A80, 11S80
  • DOI: https://doi.org/10.1090/S0002-9939-09-09991-2
  • MathSciNet review: 2515417