Seminar
Spectral properties of the finite Hilbert transform on two adjacent intervals via the method of Riemann-Hilbert problem
by Elliot Blackstone (KTH)
Location: 200B.02.18, Leuven
Time: Tuesday December 3, 2019 at
14:00
In this talk we discuss the spectra of bounded self-adjoint linear operators that are related to finite Hilbert transforms \(\mathcal{H}_L:L^2([b_L,0])\to L^2([0,b_R])\) and \( \mathcal{H}_R:L^2([0,b_R])\to L^2([b_L,0]).\) These operators arise when one studies the interior problem of tomography. The diagonalization of \(\mathcal{H}_R,\mathcal{H}_L\) has been previously obtained, but only asymptotically when \(b_L\neq-b_R\). We implement a novel approach based on the method of matrix Riemann-Hilbert problems (RHP) which diagonalizes \(\mathcal{H}_R,\mathcal{H}_L\) explicitly. We also find the asymptotics of the solution to a related RHP and obtain error estimates.
