منابع مشابه
A Support Theorem for the Geodesic Ray Transform of Functions
Let (M, g) be a simple Riemannian manifold. Under the assumption that the metric g is real-analytic, it is shown that if the geodesic ray transform of a function f ∈ L(M) vanishes on an appropriate open set of geodesics, then f = 0 on the set of points lying on these geodesics. Using this result, a version of Helgason’s support theorem for the geodesic ray transform is proven. The approach is b...
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In this article a review on the definition of the X- ray transform and some ofits applications in Nano crystallography is presented. We shall show that the X- raytransform is a special case of the Radon transform on homogeneous spaces when thetopological group E(n)- the Euclidean group - acts on ℝ2 transitively. First someproperties of the Radon transform are investigated then the relationship ...
متن کاملA Support Theorem for the Geodesic Ray Transform of Symmetric Tensor Fields
Let (M, g) be a simple Riemannian manifold with boundary and consider the geodesic ray transform of symmetric 2-tensor fields. Let the integral of f along maximal geodesics vanish on an appropriate open subset of the space of geodesics in M . Under the assumption that the metric g is real-analytic, it is shown that there exists a vector field v satisfying f = dv on the set of points lying on th...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1992
ISSN: 0022-247X
DOI: 10.1016/0022-247x(92)90079-s