145 citations · 843 across the 63 of their papers we have counts for
6 papers · 2 filters
Hyperelliptic uniformization of algebraic curves of the third order
A. I. Aptekarev, D. N. Toulyakov, W. Van Assche
An algebraic function of the third order plays an important role in the problem of asymptotics of Hermite-Padé approximants for two analytic functions with branch points. This alge…
On 2D discrete Schrödinger operators associated with multiple orthogonal polynomials
Alexander I Aptekarev, Maxim Derevyagin, Walter Van Assche
A class of cross-shaped difference operators on a two dimensional lattice is introduced. The main feature of the operators in this class is that their formal eigenvectors consist o…
Discrete integrable systems generated by Hermite-Padé approximants
Alexander I. Aptekarev, Maxim Derevyagin, Walter Van Assche
We consider Hermite-Padé approximants in the framework of discrete integrable systems defined on the lattice . We show that the concept of multiple orthogonality is i…
Ratio asymptotics for multiple orthogonal polynomials
Walter Van Assche
We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the recurrence coefficients in the nearest neighbor recurre…
Mehler-Heine asymptotics for multiple orthogonal polynomials
Walter Van Assche
Mehler-Heine asymptotics describe the behavior of orthogonal polynomials near the edges of the interval where the orthogonality measure is supported. For Jacobi polynomials and Lag…
Orthogonal polynomials for Minkowski's question mark function
Zoé Dresse, Walter Van Assche
Hermann Minkowski introduced a function in 1904 which maps quadratic irrational numbers to rational numbers and this function is now known as Minkowski's question mark function sin…