Details

Autor(en) / Beteiligte

• Bertola, Marco
• Blackstone, Elliot
• Katsevich, Alexander
• Tovbis, Alexander

Titel

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

Ist Teil von

• Analysis and mathematical physics, 2020, Vol.10 (3), p.27-27, Article 27

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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 ≠ - 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.