Date of Completion
4-25-2019
Embargo Period
4-25-2019
Keywords
Spherical Means, Gaussian Radon Transform, Hermite Polynomials
Major Advisor
Ambar Sengupta
Associate Advisor
Luke Rogers
Associate Advisor
Iddo Ben-Ari
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
We show in detail that the limit of spherical surface integrals taken over slices of a high dimensional sphere is a Gaussian integral on an affine plane of finite codimension in infinite dimensional space. We then utilize these ideas to show that a natural class of orthogonal polynomials on high dimensional spheres limit to Hermite polynomials.
Recommended Citation
Peterson, Amy, "Gaussian Limits and Polynomials on High Dimensional Spheres" (2019). Doctoral Dissertations. 2137.
https://digitalcommons.lib.uconn.edu/dissertations/2137
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