3 papers
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}/…
math.OC2026
Horizon-Uniform Sensitivity and Decay of Terminal Reward Perturbations in Discrete-Time Pontryagin Systems
Pyuyi Chufeng Huang, Zikang Song
We study local stationary solutions of finite-horizon discrete-time Pontryagin systems near a steady extremal. Suppose that the stationarity equation for the control is regular, th…