每个实根指数多项式都是Lee-Yang多项式的限制
Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial
AI总结：
该研究证明所有实根指数多项式都是Lee-Yang多项式在环面正直线上的限制，结合已有结论，验证了Kurasov-Sarnak基于稳定多项式的构造可覆盖全部$\mathbb{N}$值傅里叶准晶。
摘要：
Lee-Yang多项式$ p(z_{1},\ldots,z_{n}) $是指在多圆盘$ \mathbb{D}^{n} $及其逆区域$ (\mathbb{C}\setminus\overline{\mathbb{D}})^{n} $中均无零点的多项式。我们证明，任何形如$f(x) = \sum_{j=0}^s c_j e^{λ_j x}$的实根指数多项式，都可表示为某个Lee-Yang多项式在环面中正直线上的限制。结合Olevskii与Ulanovskii的前期研究，这一结果表明，Kurasov-Sarnak基于稳定多项式构造的$ \mathbb{N} $值傅里叶准晶，涵盖了所有可能的$ \mathbb{N} $值傅里叶准晶。
英文摘要：
A Lee-Yang polynomial $ p(z_{1},\ldots,z_{n}) $ is a polynomial that has no zeros in the polydisc $ \mathbb{D}^{n} $ and its inverse $ (\mathbb{C}\setminus\overline{\mathbb{D}})^{n} $. We show that any real-rooted exponential polynomial of the form $f(x) = \sum_{j=0}^s c_j e^{λ_j x}$ can be written as the restriction of a Lee-Yang polynomial to a positive line in the torus. Together with previous work by Olevskii and Ulanovskii, this implies that the Kurasov-Sarnak construction of $ \mathbb{N} $-valued Fourier quasicrystals from stable polynomials comprises every possible $ \mathbb{N} $-valued Fourier quasicrystal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
