Polynomials and high-dimensional spheres. (October 2019)

• Record Type: Journal Article
• Authors: Peterson, Amy; Sengupta, Ambar N.
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 18
• Page End: 48
• Publication Date: 2019-10
• Subjects: primary 44A12 -- secondary 28C20 60H40; Spherical harmonics -- Gaussian measures -- Spherical Laplacian; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.03.023
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We show that a natural class of orthogonal polynomials on large spheres in N dimensions tend to Hermite polynomials in the large-N limit. We determine the behavior of the spherical Laplacian as well as zonal harmonic polynomials in the large-N limit.