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

2014/11/05 by Its, A. R., Kozlowski, K. K. · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1411.1216

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 the present paper, we demonstrate that the operator-valued Riemann--Hilbert problem arising in the characterisation of so-called c-shifted integrable integral operators allows one to extract the large-x asymptotics of the Fredholm determinant associated with such operators.

Cited by

• Generalized discrete integrable operator and integrable hierarchy

Related

• On determinants of integrable operators with shifts
• Asymptotics via Steepest Descent for an Operator Riemann-Hilbert Problem
• Riemann--Hilbert Problems
• Large value estimates in number theory, harmonic analysis, and computer science
• A priori L^p estimates for solutions of Riemann-Hilbert Problems