Date of Completion
Spherical Means, Gaussian Radon Transform, Hermite Polynomials
Field of Study
Doctor of Philosophy
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.
Peterson, Amy, "Gaussian Limits and Polynomials on High Dimensional Spheres" (2019). Doctoral Dissertations. 2137.