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%T SUPPORT THEOREMS FOR CERTAIN RAY TRANSFORMS
%A Abhishek, Anuj.
%D 2018-10-09T07:38:27.197-04:00
%8 2018-10-09
%R http://localhost/files/05742452j
%X Abstract: The main object of study in this thesis are integral transforms over simple, real analytic, Riemannian manifolds. Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n >=3. The first result that we present here establishes a support theorem for the transverse ray transform of tensor fields of rank 2 defined over such manifolds. More specifically, given a symmetric tensor field f of rank 2, we show that if the transverse ray transform of f vanishes over an appropriate open set of maximal geodesics of M, then the support of f vanishes on the points of M that lie on the union of the aforementioned open set of geodesics. The second problem concerns integral moments transform of a symmetric m-tensor field on a simple, real analytic, Riemannian manifold as above. Integral moments of m-tensor field were first introduced by Sharafutdinov. At first we generalize a Helgason type support theorem proven by Krishnan and Stefanov in "A support theorem for the geodesic ray transform of symmetric tensor fields", Inverse Problems and Imaging, 3(3):453-464,2009. We use this extended result along with the first m+1-integral moments of the m-tensor field to prove an injectivity result and support theorem for such transforms.; Thesis (Ph.D.)--Tufts University, 2018.; Submitted to the Dept. of Mathematics.; Advisor: Eric Quinto.; Committee: Venkateswaran Krishnan, Fulton Gonzalez, and David Finch.; Keyword: Mathematics.
%[ 2018-10-15
%9 Text
%~ Tufts Digital Library
%W Institution