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arXiv · 2608.19676

Nonexistence of Frame Measures for Separated Uniform Consecutive-Digit Bernoulli Convolutions

Xiao-Ye Fu·Wei-Jie Wang
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Abstract

We investigate the existence problem of frame measures for uniform consecutive-digit Bernoulli convolutions under the separated scaling condition. Given parameters $N\geq 2$ and $0<\rho<1/N$, we prove that if $\rho^{-m}=B$ for some integers $m\geq 1$ and $B\geq 2$, with $N\nmid B$, then the associated $N$-Bernoulli convolution $\mu_{\rho,N}$ admits no frame measure. The proof introduces a new cyclic mask-quotient obstruction adapted to the multi-character structure of the consecutive-digit framework.

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Xiao-Ye Fu, Wei-Jie Wang. 2026-08-20. Nonexistence of Frame Measures for Separated Uniform Consecutive-Digit Bernoulli Convolutions. https://arxiv.org/abs/2608.19676

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