Spectral Analysis of the Truncated Hilbert Transform with Overlap

DOI10.1137/130910798zbMath1296.65184arXiv1302.6295OpenAlexW1977795109MaRDI QIDQ5415056

Reema al-Aifari, Alexander Katsevich

Publication date: 9 May 2014

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.6295

zbMATH Keywords

inverse problemHilbert transformspectrumSturm-Liouville problemsingular valuestomographylimited datadifferentiated back projection

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Spectrum, resolvent (47A10) Eigenvalue problems for linear operators (47A75) Green's functions for ordinary differential equations (34B27) Numerical methods for integral transforms (65R10) Numerical methods for inverse problems for integral equations (65R32) Inverse problems for integral equations (45Q05)

Related Items (14)

Solutions to inverse moment estimation problems in dimension 2, using best constrained approximation ⋮ Lower bounds for the Dyadic Hilbert transform ⋮ Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann-Hilbert approach ⋮ Diagonalization of the finite Hilbert transform on two adjacent intervals ⋮ Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach ⋮ Quantitative invertibility and approximation for the truncated Hilbert and Riesz transforms ⋮ On the commutation properties of finite convolution and differential operators. I: Commutation ⋮ Orthogonal residue sequences ⋮ 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 ⋮ Commuting integral and differential operators and the master symmetries of the Korteweg–de Vries equation ⋮ Asymptotic Analysis of the SVD for the Truncated Hilbert Transform with Overlap ⋮ On Sobolev instability of the interior problem of tomography ⋮ Ill-Posed Problems: From Linear to Nonlinear and Beyond

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