发表机构
University of Oregon（俄勒冈大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了由经典盖根鲍尔、雅可比或拉盖尔多项式包裹积构成的两族多元正交多项式的加法公式，以多层积分显式表示，从而将域上傅里叶展开分析简化为一变量情形。
AI 中文摘要
加法公式是多元正交多项式再生核的闭式公式；后者是正交投影算子的核。我们推导了两个正交多项式族的加法公式，这些多项式由单位球上的经典盖根鲍尔多项式与单纯形上的经典雅可比多项式或乘积拉盖尔多项式的包裹积组成，每个公式均明确地表示为单变量经典正交多项式积分的多层形式。这些公式为分析提供了有力工具，并使我们能够将域上傅里叶正交展开的大量分析简化为一变量分析。
英文摘要
An addition formula is a closed-form formula for reproducing kernels of orthogonal polynomials of several variables; the latter are kernels of orthogonal projection operators. We derive addition formulas for two families of orthogonal polynomials, which consist of wrapped products of classical Gegenbauer polynomials on the unit ball with either classical Jacobi polynomials on the simplex or product Laguerre polynomials, each of which is given explicitly as a multilayer of integrals of a classical orthogonal polynomial of one variable. These formulas provide a powerful tool for analysis and allow us, in particular, to reduce a substantial portion of analysis on the Fourier orthogonal expansions on the domains to that of one variable.
