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.

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