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math.FA2026
Nonexistence of Frame Measures for Separated Uniform Consecutive-Digit Bernoulli Convolutions
Xiao-Ye Fu, Wei-Jie Wang
We investigate the existence problem of frame measures for uniform consecutive-digit Bernoulli convolutions under the separated scaling condition. Given parameters and $0…
math.FA2026
Rational Spectra for Finite Hadamard Pairs and Bounded Spectral Sets on the real line
Xiao-Ye Fu, Zi-Jian Song
We prove that every finite spectral pair \((A,Γ)\) with \(A\subset\mathbb Z\), \(Γ\subset\mathbb R/\mathbb Z\), and \(0\inΓ\) has a rational spectrum, that is, \(Γ\subset\mathbb Q/…
math.FA2026
A Walsh-Quotient Obstruction for Fourier Frames on Odd Reciprocal-Power Bernoulli Convolutions
Xiao-Ye Fu, Zi-Jian Song, Wei-Jie Wang
We introduce a Walsh--quotient obstruction to study Fourier-frame existence for symmetric two-branch Bernoulli convolutions \[ μ_{ρ,d} =\ast_{j=1}^{\infty} \frac12\bigl(δ_{-dρ^{j}/…