A support theorem for the X-ray transform
نویسندگان
چکیده
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...
متن کاملThe X-ray Transform and its Application in Nano Crystallography
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...
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl Transform
Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1992
ISSN: 0022-247X
DOI: 10.1016/0022-247x(92)90079-s