A Support Theorem for a Gaussian Radon Transform in Infinite Dimensions
نویسندگان
چکیده
We prove that in infinite dimensions, if a bounded 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.
منابع مشابه
The Radon-gauss Transform
Gaussian measure is constructed for any given hyperplane in an infinite dimensional Hilbert space, and this is used to define a generalization of the Radon transform to the infinite dimensional setting, using Gauss measure instead of Lebesgue measure. An inversion formula is obtained and a support theorem proved.
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تاریخ انتشار 2009