10 papers
Zeros of Laurent multiple orthogonal polynomials on the unit circle
Rostyslav Kozhan, Marcus Vaktnäs
We investigate two distinct formulations of Laurent multiple orthogonal polynomials on the unit circle, introduced in arXiv:2410.12094 and arXiv:2601.04783 respectively. For the fi…
Determinantal Formulas for Rational Perturbations of Multiple Orthogonality Measures
Rostyslav Kozhan, Marcus Vaktnäs
Given multiple orthogonal polynomials on the real line with respect to a system , we investigate multiple orthogonal polynomials associated with any rat…
SzegŠMapping and Hermite--Padé Polynomials for Multiple Orthogonality on the Unit Circle
Rostyslav Kozhan, Marcus Vaktnäs
We investigate generalized Laurent multiple orthogonal polynomials on the unit circle satisfying simultaneous orthogonality conditions with respect to probability measures or l…
Angelesco and AT systems on the Unit Circle
Rostyslav Kozhan, Marcus Vaktnäs
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 establi…
Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients
Rostyslav Kozhan, František Štampach
We study asymptotic behavior of orthogonal polynomials on the unit circle with varying Verblunsky coefficients when the ratio converges as . First, w…
Christoffel Transform and Multiple Orthogonal Polynomials
Rostyslav Kozhan, Marcus Vaktnäs
We investigate multiple orthogonal polynomials associated with the system of measures obtained by applying a Christoffel transform to each of the orthogonality measures. We present…