The optimal recovery of a function from an inaccurate information on its k-plane transform. (26th April 2016) - Bagramyan, Tigran
Abstract: We consider the optimal recovery of the β th degree of the Laplacian value on a function from the information on its k -plane transform, measured with an error. We present the error of the optimal recovery and the set of optimal methods on classes with the bounded α th degree of the Laplacian, where 0 ≤ β < α . As a consequence, we give one inequality for the norms of the degree of the Laplace operator and the k -plane transform. Particular cases include new inversion methods and inequalities for the classical Radon and x-ray transforms.