保椭圆、正、非负多项式的线性算子的分类
Classifications of linear operators preserving elliptic, positive and non-negative polynomials
摘要：
我们刻画了一元实多项式的有限维或无限维空间上的所有线性算子分别保持椭圆、正、非负多项式的集合。这是通过Fischer-Fock对偶，Hankel形式和非负测度的卷积来完成的。我们还建立了这些结果的高维类似物。特别地，我们的分类定理解决了在[9]中提出的问题，这些问题起源于整函数理论和与希尔伯特第17问题有关的文献。
英文摘要：
We characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of Fischer-Fock dualities, Hankel forms, and convolutions with non-negative measures. We also establish higher-dimensional analogs of these results. In particular, our classification theorems solve the questions raised in [9] originating from entire function theory and the literature pertaining to Hilbert's 17th problem.
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。
