Related papers: On Hall-Littlewood polynomials
We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005].
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
The Hardy--Littlewood inequality for $m$-homogeneous polynomials on $\ell_{p}$ spaces is valid for $p>m.$ In this note, among other results, we present an optimal version of this inequality for the case $p=m.$ We also show that the optimal…
In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy--Littlewood constants for $2$-homogeneous polynomials on $\ell_p^2$ spaces, $2<p\leq\infty$…
In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.
We prove the existence of Hall polynomials for $x^2$-bounded invariant subspaces of nilpotent linear operators.
We study the Gaussent-Littelmann formula for Hall-Littlewood polynomials and we develop combinatorial tools to describe the formula in a purely combinatorial way for type A_n, B_n and C_n. This description is in terms of Young tableaux and…
We revisit the Bohnenblust--Hille multilinear and polynomial inequalities and prove some new properties. Our main result is a multilinear version of a recent result on polynomials whose monomials have a uniformly bounded number of…
Using the action of the Yang-Baxter elements of the Hecke algebra on polynomials, we define two bases of polynomials in n variables. The Hall-Littlewood polynomials are a subfamily of one of them. For q=0, these bases specialize into the…
We give a survey of the analytic theory of matrix orthogonal polynomials.
We investigate the growth of the polynomial and multilinear Hardy--Littlewood inequalities. Analytical and numerical approaches are performed and, in particular, among other results, we show that a simple application of the best known…
In this paper we describe various applications of the Riemann-Hilbert method to the theory of orthogonal polynomials on the line and on the circle.
The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
We show a general lower bound for Mean-value of Dirichlet polynomials
The best known upper estimates for the constants of the Hardy--Littlewood inequality for $m$-linear forms on $\ell_{p}$ spaces are of the form $\left(\sqrt{2}\right) ^{m-1}.$ We present better estimates which depend on $p$ and $m$. An…
A symbolic method is used to establish some properties of the Bernoulli-Barnes polynomials.
We introduce an algebra model to study higher order sum rules for orthogonal polynomials on the unit circle. We build the relation between the algebra model and sum rules, and prove an equivalent expression on the algebra side for the sum…
We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.