Academic Journal
A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels
| العنوان: | A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels |
|---|---|
| المؤلفون: | Bothner, Thomas |
| المصدر: | Bothner , T 2023 , ' A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels ' , Journal of Functional Analysis , vol. 285 , no. 12 , 110160 , pp. 1-109 . https://doi.org/10.1016/j.jfa.2023.110160 |
| سنة النشر: | 2023 |
| المجموعة: | University of Bristol: Bristol Reserach |
| مصطلحات موضوعية: | Hankel composition operators, Fredholm determinants, integrable systems, Riemann-Hilbert problems, nonlinear steepest descent method, Achiever-Kac theorems |
| الوصف: | 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 [44]. 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. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| DOI: | 10.1016/j.jfa.2023.110160 |
| الاتاحة: | https://hdl.handle.net/1983/828cbafc-1da2-4506-99a9-ae8f352883e3 https://research-information.bris.ac.uk/en/publications/828cbafc-1da2-4506-99a9-ae8f352883e3 https://doi.org/10.1016/j.jfa.2023.110160 |
| Rights: | info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.2A0EB297 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.jfa.2023.110160 |
|---|