A. Katsevich

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20162021

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math.CA2019

Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann-Hilbert approach

Marco Bertola, Elliot Blackstone, Alexander Katsevich +1

In this paper we study the spectra of bounded self-adjoint linear operators that are related to finite Hilbert transforms $H_{L} : L^{2} ([b_{L}, 0]) \to L^{2} ([0, b_{R}])$ and $\mathcal…

math.CA2016

Reconstruction algorithms for a class of restricted ray transforms without added singularities

Alexander Katsevich

Let $X$ and $X^{*}$ denote a restricted ray transform along curves and a corresponding backprojection operator, respectively. Theoretical analysis of reconstruction from the data $Xf…