6533b833fe1ef96bd129b858
RESEARCH PRODUCT
Large-x Analysis of an Operator-Valued Riemann–Hilbert Problem
Alexander ItsKarol K. Kozlowskisubject
Pure mathematicsIntegrable systemNonlinear schrodinger-equationMathematics::Complex VariablesGeneral Mathematics010102 general mathematicsMathematicsofComputing_NUMERICALANALYSIS[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Fredholm determinantImpenetrable bose-gas[ MATH.MATH-FA ] Mathematics [math]/Functional Analysis [math.FA][MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]01 natural sciencessymbols.namesakeRiemann hypothesisOperator (computer programming)[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesHilbert's problemssymbolsMethod of steepest descentRiemann–Hilbert problem010307 mathematical physics0101 mathematicsMathematicsdescription
International audience; 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 a la Deift-Zhou. In this paper, we demonstrate that the operator-valued Riemann-Hilbert problem arising in the characterization of so-called c-shifted integrable integral operators allows one to extract the large-x asymptotics of the Fredholm determinant associated with such operators.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-06-19 |