Year: 2024
Type: preprint
Abstract: We introduce the concept of Laurent multiple orthogonality on the unit circle and define Angelesco and AT systems in this setting. Using a generalized Andreief identity, we establish normality of all multi-indices for any such system, thereby ensuring existence and uniqueness of Laurent multiple orthogonal polynomials of type I and type II at every location. As an application, we demonstrate existence and uniqueness of the approximants for two natural two-point Hermite-Padé problems -- type I and type II -- arising in the simultaneous rational approximation of $r$ Carathéodory functions.
Source: arXiv (Cornell University)
Authors: Kozhan, Rostyslav, Vaktnäs, Marcus
Institution: Uppsala University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403577592