Related papers: On Bivariate Jacobi Konhauser Polynomials
In this work, a sequence of orthonormal rational functions that is also biorthogonal to another sequence of rational functions arising from recurrence relations of $R_{II}$ type is constructed. The biorthogonality is proved by a procedure…
We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyze relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the…
We study the properties and asymptotics of the Jacobi matrices associated with equilibrium measures of the weakly equilibrium Cantor sets. These family of Cantor sets were defined and different aspects of orthogonal polynomials on them were…
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
Kazhdan-Lusztig polynomials are important and mysterious objects in representation theory. Here we present a new formula for their computation for symmetric groups based on the Bruhat graph. Our approach suggests a solution to the…
We provide an explicit spectral representation for several weighted Hankel matrices by means of the so called commutator method. These weighted Hankel matrices are found in the commutant of Jacobi matrices associated with orthogonal…
Based on the combinatorial description of the moduli spaces of curves provided by Strebel differentials, Witten and Kontsevich have introduced combinatorial cohomology classes $W_{(m_0,m_1,m_2,\dots),n}$, and conjectured that these can be…
Dual third order Jacobsthal and dual third order Jacobsthal-Lucas numbers are defined. In this study, we work on these dual numbers and we obtain the properties e.g. some quadratic identities, summation, norm, negadual third order…
Classical orthogonal polynomial systems of Jacobi, Hermite, Laguerre and Bessel have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a classical theorem by…
In 1999, Grunbaum, Haine and Horozov defined a large family of commutative algebras of ordinary differential operators which have orthogonal polynomials as eigenfunctions. These polynomials are mutually orthogonal with respect to a…
We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras.…
A classical result due to Bochner characterizes the classical orthogonal polynomial systems as solutions of a second-order eigenvalue equation. We extend Bochner's result by dropping the assumption that the first element of the orthogonal…
We give a general method for constructing compact K\"ahler manifolds $X_1$ and $X_2$ whose intermediate Jacobians $J^k(X_1)$ and $J^k(X_2)$ are isogenous for each $k$, and we exhibit some examples. The method is based upon the algebraic…
Our goal is to find asymptotic formulas for orthonormal polynomials $P_{n}(z)$ with the recurrence coefficients slowly stabilizing as $n\to\infty$. To that end, we develop spectral theory of Jacobi operators with long-range coefficients and…
We analyze a random lozenge tiling model of a large regular hexagon, whose underlying weight structure is periodic of period $2$ in both the horizontal and vertical directions. This is a determinantal point process whose correlation kernel…
Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the…
Given a bivariate weight function defined on the positive quadrant of $\mathbb{R}^2$, we study polynomials in two variables orthogonal with respect to varying measures obtained by special modifications of this weight function. In…
We study a family of orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue equation involving a third order differential operator of Dunkl-type. The orthogonality measure of these polynomials consists…
We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are…
We present the most general polynomial Lie algebra generated by a second order integral of motion and one of order M, construct the Casimir operator, and show how the Jacobi identity provides the existence of a realization in terms of…