Stable polynomials and crystalline measures

Abstract

Explicit examples of {\bf positive} crystalline measures and Fourier quasicrystals are constructed using pairs of stable of polynomials, answering several open questions in the area.

15 pages, 1 figure

References in corpus (7)

• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
• Can One Hear the Shape of a Graph?
• On the level spacing distribution in quantum graphs
• The Lee-Yang and Pólya-Schur Programs. I. Linear Operators Preserving Stability
• Quasicrystals and Poisson's summation formula
• Fourier interpolation on the real line
• Fourier quasicrystals and discreteness of the diffraction spectrum

Cited by in corpus (8)

• Perturbed interpolation formulae and applications
• Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial
• Crystalline temperate distributions with uniformly discrete support and spectrum
• Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties
• Taylor coefficients and zeroes of entire functions of exponential type
• Discrete nonlinear Fourier transforms and their inverses
• Stability of shifts, interpolation, and crystalline measures
• Measures, modular forms, and summation formulas of Poisson type