منابع مشابه
The Radon Transform on Distributions
In the literature there are three apparently different definitions of the Radon transform on various spaces of distributions: Gelfand-Graev’s, Helgason’s and Ludwig’s. In this paper a new definition of the Radon transform on the space of the tempered distributions is given and it is proved that, properly understood, the earlier definitions are all equivalent to the new one. A constructive descr...
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 کاملOn Non-abelian Radon Transform. *
We consider the inverse prolem of the recovery of a gauge field in R 2 modulo gauge transformations from the non-abelian Radon transform. A global uniqueness theorem is proven for the case when the gauge field has a compact support. Extensions to the attenuated non-abelian Radon transform in R 2 and applications to the inverse scattering problem for the Schrödinger equation in R 2 with non-comp...
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 Japan Academy, Series A, Mathematical Sciences
سال: 1995
ISSN: 0386-2194
DOI: 10.3792/pjaa.71.202