Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach

DOI10.1002/cpa.21547zbMath1348.44003arXiv1402.0216OpenAlexW2037427584MaRDI QIDQ2790836

Marco Bertola, Alexander Tovbis, Alexander Katsevich

Publication date: 8 March 2016

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0216

zbMATH Keywords

error estimatetomographysingular valueRiemann theta functionsfinite Hilbert transformasymptotic resultmatrix Riemann-Hilbert problemsteepest-decent method

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15)

Related Items

Maximal amplitudes of finite-gap solutions for the focusing nonlinear Schrödinger equation ⋮ A scalar Riemann-Hilbert problem on the torus: applications to the KdV equation ⋮ Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann-Hilbert approach ⋮ Inversion formula and range conditions for a linear system related with the multi‐interval finite Hilbert transform in L² ⋮ Fine spectra of the finite Hilbert transform in function spaces ⋮ Diagonalization of the finite Hilbert transform on two adjacent intervals ⋮ Spectral analysis and decomposition of normal operators related with the multi-interval finite Hilbert transform ⋮ On the spectral properties of the Hilbert transform operator on multi-intervals ⋮ On Sobolev instability of the interior problem of tomography

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