Large-x analysis of an operator valued Riemann–Hilbert problem

Abstract

The purpose of this paper is to push forward the theory of operator-valued Riemann–Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method á la Deift–Zhou. In this paper, we demonstrate that the operator-valued Riemann–Hilbert problem arising in the characterization of so-called cc-shifted integrable integral operators allows one to extract the large-xx asymptotics of the Fredholm determinant associated with such operators.