RANDOM p-ADIC RIESZ PRODUCTS: CONTINUITY, SINGULARITY, AND DIMENSION

Resource
Proceedings of American Math Society,137,3477-3486.
Journal
Proceedings of the American Mathematical Society
Pages
3477
Date Issued
2009-10
Date
2009-10
Author(s)
Shieh, N.R.
Zhang, X.Y.
DOI
URI
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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journal article
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