A support theorem for a Gaussian Radon transform in infinite dimensions

Becnel, Jeremy; Sengupta, Ambar

doi:10.1090/S0002-9947-2011-05365-1

A support theorem for a Gaussian Radon transform in infinite dimensions
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by Jeremy J. Becnel and Ambar N. Sengupta PDF

Trans. Amer. Math. Soc. 364 (2012), 1281-1291 Request permission

Abstract:

We prove that in infinite dimensions, if a bounded, suitably continuous, function has zero Gaussian integral over all hyperplanes outside a closed bounded convex set, then the function is zero outside this set. This is an infinite-dimensional form of the well-known Helgason support theorem for Radon transforms in finite dimensions.

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