$S$-nodes, factorisation of spectral matrix functions and corresponding inequalities
Classical Analysis and ODEs
2026-04-29 v1 Complex Variables
Functional Analysis
Spectral Theory
Abstract
Using factorisation and Arov-Krein inequality results, we derive important inequalities (in terms of -nodes) in interpolation problems.
Cite
@article{arxiv.2404.02094,
title = {$S$-nodes, factorisation of spectral matrix functions and corresponding inequalities},
author = {Alexander Sakhnovich},
journal= {arXiv preprint arXiv:2404.02094},
year = {2026}
}
Comments
Dedicated to the memory of V.E. Katsnelson. The paper is related to the earlier works "On a class of extremal problems", Math. USSR- Izv. 30, 411--418 (1988) and "Dirac systems: asymptotic relations, Weyl functions and Toeplitz matrices", arXiv:1912.05213 by the author. Important considerations from those papers are generalised and first time completely proved in this preprint