منابع مشابه
RADON TRANSFORM ON FINITE SYMMETRIC SPACESElinor
The Radon transform belongs to the area of Inverse Problems. The reconstruction of a function from its projection or averages is a central point of study. Besides having direct applications in medical tomography, geophysics, there are also applications in signal processing, statistics and probability. Hence, it is useful to consider discretized versions of the Radon transform.
متن کاملRadon Transform on Symmetric Matrix Domains
Let X be the matrix unit ball in Mn−k,k(K) consisting of contractive matrices where K = R, C, H. The domain X is a realization of the symmetric space G/K with G = U(n− k, k; K). The matrix ball yo of lower dimension in Mk′−k,k with k ′ ≤ n is a totally geodesic submanifold of X and let Y be the manifold of all G-translations of the submanifold y0. We consider the Radon transform from functions ...
متن کاملThe Abel, Fourier and Radon transforms on symmetric spaces
In this paper we prove some recent results on the three transforms in the title and discuss their relationships to older results. The spaces we deal with are symmetric spaces X = G/K of the noncompact type, G being a connected noncompact semisimple Lie group with finite center and K a maximal compact subgroup. For the two natural Radon transforms on X we prove a new inversion formula and a shar...
متن کاملOn the Funk Transform on Compact Symmetric Spaces
We prove that a function on an irreducible compact symmetric space M which is not a sphere is determined by its integrals over the shortest closed geodesics in M . We also prove a support theorem for the Funk transform on rank one symmetric spaces which are not spheres.
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...
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ژورنال
عنوان ژورنال: Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics
سال: 1969
ISSN: 1883-2172,0373-6385
DOI: 10.2206/kyushumfs.23.159