• Corpus ID: 249191657

A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels

@inproceedings{Bothner2022ARA,
  title={A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels},
  author={Thomas Bothner},
  year={2022}
}

• Thomas Bothner
• Published 30 May 2022
• Mathematics

We characterize Fredholm determinants of a class of Hankel composition operators via matrix-valued Riemann-Hilbert problems, for additive and multiplicative compositions. The scalar-valued kernels of the underlying integral operators are not assumed to display the integrable structure known from the seminal work of Its, Izergin, Korepin and Slavnov \cite{IIKS}. Yet we are able to describe the corresponding Fredholm determinants through a naturally associated Riemann-Hilbert problem of Zakharov-Shabat type by solely exploiting the kernels' Hankel composition structures. We showcase the efficiency of this approach through a series of examples, we then compute several rank one perturbed determinants in terms of Riemann-Hilbert data and finally derive Akhiezer-Kac asymptotic theorems for suitable kernel classes.