Abstract

Atelier
« Asymptotiques des systèmes intégrables, matrices aléatoires et processus aléatoires, et universalité.
Un hommage à l’occasion du e anniversaire de Percy Deift »
– juin 
Workshop
“Asymptotics in integrable systems, random matrices and random processes and universality:
In honour of Percy Deift’s th birthday”
June –, 
Singular value decomposition of a finite Hilbert
transform defined on several intervals and the
interior problem of tomography: the
Riemann-Hilbert problem approach
Alexander Tovbis*
[email protected]
We study the asymptotics of singular values and singular functions of a Finite Hilbert transform (FHT), which is defined on several intervals. Transforms of this kind arise in the
study of the interior problem of tomography. We suggest a novel approach based on the
technique of the matrix Riemann–Hilbert problem and the steepest descent method of
Deift–Zhou.
This is joint work with Marco Bertola and Alexander Katsevich.
* Department
of Mathematics, University of Central Florida, Building: MAP Office 218, P. O. Box 160000,
Orlando, FL 32816, USA.