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- Bertola, Marco, et al.
(författare)
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Diagonalization of the finite Hilbert transform on two adjacent intervals : the Riemann-Hilbert approach
- 2020
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Ingår i: Analysis and Mathematical Physics. - : Springer Nature. - 1664-2368 .- 1664-235X. ; 10:3
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Tidskriftsartikel (refereegranskat)abstract
- 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]) -> L-2([0, b(R)]) and H-R : L-2([0, b(R)]) -> L-2([b(L), 0]). These operators arise when one studies the interior problem of tomography. The diagonalization of H-R, H-L has been previously obtained, but only asymptotically when b(L) not equal -b(R). We implement a novel approach based on the method of matrix Riemann-Hilbert problems (RHP) which diagonalizes H-R, H-L explicitly. We also find the asymptotics of the solution to a related RHP and obtain error estimates.
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