An Inversion Formula for the Gaussian Radon Transform for Banach Spaces
Irina Holmes
TL;DR
This paper introduces an inversion formula for the Gaussian Radon transform in Banach spaces, utilizing the Segal-Bargmann transform to reconstruct functions from their Gaussian Radon transform.
Contribution
It presents a disintegration theorem for the Gaussian Radon transform and a novel procedure to recover functions using the Segal-Bargmann transform in abstract Wiener spaces.
Findings
Disintegration theorem for Gaussian Radon transform
Inversion procedure using Segal-Bargmann transform
Reconstruction of functions from Gaussian Radon transform
Abstract
We provide a disintegration theorem for the Gaussian Radon transform Gf on Banach spaces and use the Segal-Bargmann transform on abstract Wiener spaces to find a procedure to obtain f from its Gaussian Radon transform Gf.
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