A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels
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Publication:6072351
DOI10.1016/J.JFA.2023.110160arXiv2205.15007MaRDI QIDQ6072351
Author name not available (Why is that?)
Publication date: 13 October 2023
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/2205.15007
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