Related papers: Parameters associated with bivariate Bernstein-Sze…

In this paper we study quasi-orthogonality on the unit circle based on the structural and orthogonal properties of a class of self-invariant polynomials. We discuss a special case in which these polynomials are represented in terms of the…

Let p(t) be a trigonometric polynomial, non-negative on the unit circle. We say that a measure \sigma belongs to a polynomial Szego class, if the logarithm of its density is summable over the circle with the weight p(t). For the associated…

We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations. It is shown that the coefficients in these recurrence relations…

In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…

Given a measure $\mu$ on the unit sphere $\partial\mathbb{B}^d$ in $\mathbb{C}^d$ with Lebesgue decomposition ${\rm d} \mu = w \, {\rm d} \sigma + {\rm d} \mu_s$, with respect to the rotation-invariant Lebesgue measure $\sigma$ on $\partial…

For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the…

We show that Bernstein polynomials are related to the Lebesgue measure on [0, 1] in a manner similar as Chebyshev polynomials are related to the equilibrium measure of [--1, 1]. We also show that Pell's polynomial equation satisfied by…

This paper studies recurrence phenomena in iterative holomorphic dynamics of certain multi-valued maps. In particular, we prove an analogue of the Poincar\'e recurrence theorem for meromorphic correspondences with respect to certain…

Let $d\nu$ be a measure in $\mathbb{R}^d$ obtained from adding a set of mass points to another measure $d\mu$. Orthogonal polynomials in several variables associated with $d\nu$ can be explicitly expressed in terms of orthogonal polynomials…

It is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five-diagonal matrices depending on the Schur parameters. This result is achieved through the study of orthogonal Laurent…

We study the moment space corresponding to matrix measures on the unit circle. Moment points are characterized by non-negative definiteness of block Toeplitz matrices. This characterization is used to derive an explicit representation of…

We study multiple orthogonal polynomials of type I and type II which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the…

We study different pointwise recurrence notions for linear dynamical systems from the Ergodic Theory point of view. We show that from any reiteratively recurrent vector $x_0$, for an adjoint operator $T$ on a separable dual Banach space…

We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers of the second kind that we studied in a previous work. We prove the bi-variate poly-Bernoulli polynomial version of some known results on…

We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for…

Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular, we examine the relations between the measure of concordance of an $n$-copula and the…

In this work, tests of symmetry for bivariate copulas are introduced and studied using empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a multiplier bootstrap…

In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…

This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…

In this survey article, we review some results and conjectures related to orthogonal polynomials on Cantor sets. The main purpose of this paper is to emphasize the role of equilibrium measures in order to have a general theory of…