The Malgrange Form and Fredholm Determinants

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Author: Bertola, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148566
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Malgrange Form and Fredholm Determinants / M. Bertola // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 15 назв. — англ.

We consider the factorization problem of matrix symbols relative to a closed contour, i.e., a Riemann-Hilbert problem, where the symbol depends analytically on parameters. We show how to define a function τ which is locally analytic on the space of deformations and that is expressed as a Fredholm de...