A Gaussian Radon Transform for Banach Spaces

TL;DR

This paper introduces a Gaussian Radon transform tailored for Banach spaces, establishing a uniqueness theorem for functions based on their integrals over hyperplanes outside a convex set.

Contribution

It develops a new Radon transform for Banach spaces using Gaussian measures and proves a uniqueness result for functions based on hyperplane integrals.

Findings

Uniqueness of functions determined by Gaussian hyperplane integrals

Extension of Radon transform concepts to Banach spaces

Theoretical foundation for Gaussian Radon transforms in infinite-dimensional spaces

Abstract

We develop a Radon transform on Banach spaces using Gaussian measure and prove that if a bounded continuous function on a separable Banach space has zero Gaussian integral over all hyperplanes outside a closed bounded convex set in the Hilbert space corresponding to the Gaussian measure then the function is zero outside this set.