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.
متن کاملThe Gaussian Radon Transform for Banach Spaces
The classical Radon transform can be thought of as a way to obtain the density of an n-dimensional object from its (n− 1)-dimensional sections in di erent directions. A generalization of this transform to in nite-dimensional spaces has the potential to allow one to obtain a function de ned on an in nite-dimensional space from its conditional expectations. We work within a standard framework in ...
متن کاملThe Radon Transform on Z *
where S + x denotes the setf-s + x i s e S ) . Thus, the Radon transform can be thought of as a way of replacing/by a "smeared out" version of /. This form of the transform represents a simplified model of the kind of averaging which occurs in certain applied settings, such as various types of tomography and recent statistical averaging techniques. A fundamental question which arises in connect...
متن کاملThe Radon Transform on Zn
The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore-Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.
متن کاملThe Radon Transform on Z
The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore–Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.2307/2159713