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Holmgren’s uniqueness theorem and support theorems for real analytic Radon transforms. (English) Zbl 0791.44003

Grinberg, Eric L. (ed.), Geometric analysis. Proceedings of an AMS special session, held at the 868th meeting of the American Mathematical Society at Temple University, Philadelphia, PA, USA, October 12-13, 1991. Providence, RI: American Mathematical Society. Contemp. Math. 140, 23-30 (1992).
Holmgren’s uniqueness theorem and support theorems for real analytic Radon transforms are proved. The generalized Radon transform is defined as \(R_ \rho f(H)=\int_ H f (x) \rho (x,H)ds\), assuming the weight function \(\rho\) is positive and real analytic, \(ds\) is the Euclidean surface measure on the hyperplane \(H\), and integration is to be performed w.r.t. \(x\). The proof of the main theorem depends on microlocal regularity properties of solutions to the equation \(R_ \rho f=0\) together with a recent vanishing theorem by the author.
For the entire collection see [Zbl 0773.00025].
Reviewer: S.P.Goyal (Jaipur)

MSC:

44A12 Radon transform
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
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