AI 中文总结
该研究将正整数质量的傅里叶拟晶体测度刻画为带加权局部相交度的有效李-杨循环的实截面，回答了相关问题，通过谱重构代数解析集等完成证明，揭示奇异李-杨截面的性质。
AI 中文摘要
我们将具有正整数质量的傅里叶拟晶体测度刻画为有效李-杨循环的实截面，带有加权局部相交度。截面矩阵具有正的极大子式，每个根处的质量为其加权局部相交度。对于Delone支撑，可选择循环的约化支撑为严格的。每个整数质量傅里叶拟晶体测度的支撑是有限个实值三角多项式的公共复零点集。对于单位质量，可选择表示循环为约化的，每个物理根处的局部度为1。这些结果回答了Alon、Kummer、Kurasov和Vinzant的问题(1)、(2)和(4)。证明从谱中恢复有限维环面，证明所得解析集是代数的，并从矩中重构其复分支及其整数系数。完整序列的支撑高度定理给出所需的线性谱界。奇异李-杨截面是带有其自然局部相交度的傅里叶拟晶体测度；丢弃这些度会破坏傅里叶拟晶体性质。
英文摘要
We characterize Fourier quasicrystal measures with positive integer masses as real sections of effective Lee-Yang cycles, with weighted local intersection degrees. The section matrix has positive maximal minors, and the mass at each root is its weighted local intersection degree. For Delone support the reduced support of the cycle can be chosen strict. The support of every integer-mass Fourier quasicrystal measure is the common complex zero set of finitely many real-valued trigonometric polynomials. For unit masses the representing cycle can be chosen reduced, with local degree one at every physical root. These results answer Questions (1), (2), and (4) of Alon, Kummer, Kurasov, and Vinzant. The proof recovers a finite-dimensional torus from the spectrum, proves that the resulting analytic set is algebraic, and reconstructs its complex branches and their integer coefficients from their moments. A support-height theorem for holonomic sequences gives the required linear spectral bound. Singular Lee-Yang sections are Fourier quasicrystal measures with their natural local intersection degrees; discarding those degrees can destroy the Fourier quasicrystal property.
Comments67 pages
