6533b7d0fe1ef96bd125b69c

RESEARCH PRODUCT

On Determinants of Integrable Operators with Shifts

Alexander ItsKarol K. Kozlowski

subject

Semi-elliptic operatorPure mathematicsOperator (computer programming)Multiplication operatorIntegrable systemGeneral MathematicsMathematical analysisFinite-rank operatorOperator theoryCompact operatorMathematicsQuasinormal operator

description

Integrable integral operator can be studied by means of a matrix Riemann--Hilbert problem. However, in the case of so-called integrable operators with shifts, the associated Riemann--Hilbert problem becomes operator valued and this complicates strongly the analysis. In this note, we show how to circumvent, in a very simple way, the use of such a setting while still being able to characterize the large-$x$ asymptotic behavior of the determinant associated with the operator.

yearjournalcountryeditionlanguage
2013-09-06International Mathematics Research Notices
https://doi.org/10.1093/imrn/rnt191