29 citations · 142 across the 28 of their papers we have counts for
22 papers · 1 filter
A unified approach via Geronimus transformation to various types of orthogonal polynomials
Maxim Derevyagin, Juan Carlos García Ardila
We present a unified Geronimus-type construction that leads to various orthogonal polynomials including indefinite orthogonal polynomials, exceptional and, more generally, lacunary…
A remark on Chebyshev rational functions, multipoint Padé approximants and Noise
Maxim Derevyagin, Max Meynig
Motivated by the recent interest in multipoint Padé approximants in the physics community, we discuss Chebyshev rational functions and show how they give rise to multipoint Padé ap…
Complex Jacobi matrices generated by Darboux transformations
Rachel Bailey, Maxim Derevyagin
In this paper, we study complex Jacobi matrices obtained by the Christoffel and Geronimus transformations at a nonreal complex number, including the properties of the corresponding…
A note on an asymptotic formula for integrals of products of Jacobi polynomials
Maxim Derevyagin, Nicholas Juricic
We recast Byerly's formula for integrals of products of Legendre polynomials. Then we adopt the idea to the case of Jacobi polynomials. After that, we use the formula to derive an…
A Theorem of Joseph-Alfred Serret and its Relation to Perfect Quantum State Transfer
Maxim Derevyagin, Anastasiia Minenkova, Nathan Sun
In this paper we recast the Serret theorem about a characterization of palindromic continued fractions in the context of polynomial continued fractions. Then, using the relation be…
Jacobi matrices generated by ratios of hypergeometric functions
Maxim Derevyagin
A problem of determining zeroes of the Gauss hypergeometric function goes back to Klein, Hurwitz, and Van Vleck. In this very short note we show how ratios of hypergeometric functi…
Asymptotics for polynomials orthogonal in an indefinite metric
Maxim Derevyagin, Brian Simanek
We continue studying polynomials generated by the Szegő recursion when a finite number of Verblunsky coefficients lie outside the closed unit disk. We prove some asymptotic results…
A note on Wall's modification of the Schur algorithm and linear pencils of Jacobi matrices
Maxim Derevyagin
In this note we revive a transformation that was introduced by H. S. Wall and that establishes a one-to-one correspondence between continued fraction representations of Schur, Cara…
On Szegő's theorem for a nonclassical case
Maxim Derevyagin, Brian Simanek
In this paper we prove Szegő's Theorem for the case when a finite number of Verblunsky coefficients lie outside the closed unit disk. Although a form of this result was already pro…
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…
Multiple Geronimus transformations
Maxim Derevyagin, Juan Carlos García-Ardila, Francisco Marcellán
We consider multiple Geronimus transformations and show that they lead to discrete (non-diagonal) Sobolev type inner products. Moreover, it is shown that every discrete Sobolev inn…
A note on the Geronimus transformation and Sobolev orthogonal polynomials
Maxim Derevyagin, Francisco Marcellán
In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus tran…
On the relation between Darboux transformations and polynomial mappings
Maxim Derevyagin
Let dμ(t) be a probability measure on [0,+\infty) such that its moments are finite. Then the Cauchy-Stieltjes transform S of dμ(t) is a Stieltjes function, which admits an expansio…
CMV matrices and little and big -1 Jacobi polynomials
Maxim Derevyagin, Luc Vinet, Alexei Zhedanov
We introduce a new map from polynomials orthogonal on the unit circle to polynomials orthogonal on the real axis. This map is closely related with the theory of CMV matrices. It co…
Szegő's theorem for matrix orthogonal polynomials
Maxim Derevyagin, Olga Holtz, Sergey Khrushchev +1
We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szegő's theorem. As a…
Darboux transformations of Jacobi matrices and Padé approximation
Maxim Derevyagin, Vladimir Derkach
Let J be a monic Jacobi matrix associated with the Cauchy transform F of a probability measure. We construct a pair of the lower and upper triangular block matrices L and U such th…
Inverse problems for periodic generalized Jacobi matrices
Maxim Derevyagin
Some inverse problems for semi-infinite periodic generalized Jacobi matrices are considered. In particular, a generalization of the Abel criterion is presented. The approach is bas…
The Jacobi matrices approach to Nevanlinna-Pick problems
Maxim Derevyagin
A modification of the well-known step-by-step process for solving Nevanlinna-Pick problems in the class of $\bR_0$-functions gives rise to a linear pencil , where and …
The linear pencil approach to rational interpolation
Bernhard Beckermann, Maxim Derevyagin, Alexei Zhedanov
It is possible to generalize the fruitful interaction between (real or complex) Jacobi matrices, orthogonal polynomials and Pade approximants at infinity by considering rational in…
Convergence of diagonal Padé approximants for a class of definitizable functions
Maxim Derevyagin, Vladimir Derkach
Convergence of diagonal Padé approximants is studied for a class of functions which admit the integral representation $ {\mathfrak F}(λ)=r_1(λ)\int_{-1}^1\frac{tdσ(t)}{t-λ}+r_2(λ),…
An operator approach to multipoint Pade approximations
Maxim S. Derevyagin, Alexei S. Zhedanov
First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-ste…