凸多面体到直线的投影及更高一维普朗克系统
Projections of convex polytopes to a line and higher univariate Prony systems
AI总结：
研究凸多面体勒贝格测度到直线的推前，揭示其作为分段多项式密度的性质，并引入更高维普朗克系统，解决逆动量问题。
摘要：
受凸多面体逆动量问题启发，我们研究凸d-多面体上勒贝格测度到直线的推前。此类推前是分段多项式密度，其动量自然导出一族『更高』一维普朗克系统，当d=0时还原为经典普朗克系统。我们描述了对应的固定节点分段多项式锥，给出了显式的振幅恢复准则，记录了归一化动量的有理生成函数和递推关系，并将方向动量流形与出现在多面体上测度的动量流形理论中的Hankel行列式流形相识别。
英文摘要：
Motivated by the inverse moment problem for convex polytopes, we study the pushforward to a line of the Lebesgue measure restricted to a convex $d$-polytope. Such pushforwards are spline densities of degree $d-1$, and their moments lead naturally to a family of ``higher'' univariate Prony systems, with the classical Prony system recovered when $d=0$. We describe the corresponding fixed-knot spline cone, give an explicit amplitude recovery criterion, record the rational generating function and recurrence satisfied by the normalized moments, and identify the directional moment variety with the Hankel determinantal variety appearing in the theory of moment varieties of measures on polytopes.
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。
