[HTML][HTML] S-curves in polynomial external fields

ABJ Kuijlaars, GLF Silva - Journal of Approximation Theory, 2015 - Elsevier
Curves in the complex plane that satisfy the S-property were first introduced by Stahl and
they were further studied by Gonchar and Rakhmanov in the 1980s. Rakhmanov recently …

On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials

AI Aptekarev, GL Lagomasino… - Russian …, 2017 - iopscience.iop.org
This survey considers multiple orthogonal polynomials with respect to Nikishin systems
generated by a pair $(\sigma_1,\sigma_2) $ of measures with unbounded supports …

On two families of discrete multiple orthogonal polynomials on a star-like set

J Arvesú Carballo, AJ Quintero Roba - Lobachevskii Journal of …, 2023 - Springer
We study two families of type II discrete multiple orthogonal polynomials on an-legged star-
like set with respect to weight functions of Charlier (Poisson distributions) and Meixner …

On the q-Charlier multiple orthogonal polynomials

J Arvesú, AM Ramírez-Aberasturis - SIGMA. Symmetry, Integrability and …, 2015 - emis.de
We introduce a new family of special functions, namely $ q $-Charlier multiple orthogonal
polynomials. These polynomials are orthogonal with respect to $ q $-analogues of Poisson …

The Mhaskar–Saff variational principle and location of the shocks of certain hyperbolic equations

AI Aptekarev - Modern Trends in Constructive Function Theory …, 2016 - books.google.com
We discuss an application of the Mhaskar–Saff functional to the problem of location of the
hyperbolic shocks in the context of completely integrable approximations to nonlinear …

Multiple Meixner polynomials on a non-uniform lattice

J Arvesú, AM Ramírez-Aberasturis - Mathematics, 2020 - mdpi.com
We consider two families of type II multiple orthogonal polynomials. Each family has
orthogonality conditions with respect to a discrete vector measure. The r components of …

The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations

AI Aptekarev, DN Tulyakov - Sbornik: Mathematics, 2014 - iopscience.iop.org
Recurrence relations generating Padé and Hermite-Padé polynomials are considered. Their
coefficients increase with the index of the relation, but after dividing by an appropriate power …

Nearest Neighbor Recurrence Relations for Meixner–Angelesco Multiple Orthogonal Polynomials of the Second Kind

J Arvesú, AJ Quintero Roba - Mathematics, 2023 - mdpi.com
This paper studies a new family of Angelesco multiple orthogonal polynomials with shared
orthogonality conditions with respect to a system of weight functions, which are complex …

О системах Никишина с дискретными компонентами и слабой асимптотике многочленов совместной ортогональности

АИ Аптекарев, Г Лопес Лагомасино… - Успехи …, 2017 - mathnet.ru
В работе рассматриваются совместно ортогональные многочлены по отношению к
системам Никишина, генерируемым двумя мерами (σ1, σ2) с неограниченными …

On two families of discrete multiple orthogonal polynomials on a star-like set

JA Carballo, AJQ Roba - arXiv preprint arXiv:2312.14317, 2023 - arxiv.org
We study two families of type II discrete multiple orthogonal polynomials on an $ r $-legged
star-like set with respect to $ r $ weight functions of Charlier (Poisson distributions) and …