Integral operators with the generalized sine-kernel on the real axis
N. A. Slavnov
TL;DR
This paper investigates the asymptotic behavior of integral operators with a generalized sine kernel on the real axis, deriving formulas for the resolvent and Fredholm determinant in the large x limit, with applications to integrable models.
Contribution
It provides new asymptotic formulas for the resolvent and Fredholm determinant of these operators, advancing understanding in integrable systems.
Findings
Formulas for the resolvent in the large x limit
Expressions for the Fredholm determinant asymptotics
Applications to integrable models
Abstract
The asymptotic properties of integral operators with the generalized sine kernel acting on the real axis are studied. The formulas for the resolvent and the Fredholm determinant are obtained in the large x limit. Some applications of the results obtained to the theory of integrable models are considered.
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