4 papers
On the spectral properties of the Hilbert transform operator on multi-intervals
Marco Bertola, Alexander Katsevich, Alexander Tovbis
Let be two multi-intervals with non-intersecting interiors. Consider the following operator $$A:\, L^2( J )\to L^2(E),\ (Af)(x) = \frac 1π\int_{ J } \frac {f(…
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 and $\mathcal…
Resolution analysis of inverting the generalized Radon transform from discrete data in
Alexander Katsevich
A number of practically important imaging problems involve inverting the generalized Radon transform (GRT) of a function in . On the other hand, not m…
Reconstruction algorithms for a class of restricted ray transforms without added singularities
Alexander Katsevich
Let and denote a restricted ray transform along curves and a corresponding backprojection operator, respectively. Theoretical analysis of reconstruction from the data $Xf…