Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Sharp estimates of the Jacobi heat kernel
The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the other two classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters α, β ≥ -1/2. Using quite different methods, Coulhon, Kerkyacharian and Petrushev recently also obtained such estimates. As an application of the bounds, we show that...
Skew-orthogonal polynomials of a discrete variable.
Sobolev orthogonal polynomials: Interpolation and approximation.
Some applications and numerical methods for orthogonal polynomials
Some class of polynomial hypergroups
We provide explicit formulas for linearizing coefficients for some class of orthogonal polynomials.
Some Coefficient Estimates for Polynomials on the Unit Interval
2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.In this paper we present some inequalities about the moduli of the coefficients of polynomials of the form f (x) : = еn = 0nan xn, where a0, ј, an О C. They can be seen as generalizations, refinements or analogues of the famous inequality of P. L. Chebyshev, according to which |an| Ј 2n-1 if | еn = 0n an xn | Ј 1 for -1 Ј x Ј 1.
Some counterexamples to subexponential growth of orthogonal polynomials
We give examples of polynomials p(n) orthonormal with respect to a measure μ on ⨍ such that the sequence {p(n,x)} has exponential lower bound for some points x of supp μ. Moreover, the set of such points is dense in the support of μ.
Some discrete representations of -classical linear forms.
Some properties of orthogonal polynomials for Laguerre-type weights.
Some results on biorthogonal polynomials.
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...
Spectral Pairs in Cartesian Coordinates.
Stability and sensivity of Darboux transformation without parameter.
Strict positive definiteness on spheres via disk polynomials.
Strong asymptotics for extremal polynomials off a complex curve.
Sucesiones de polinomios ortogonales estrictamente γ-típicas.
Sufficient conditions for the spectrality of self-affine measures with prime determinant
Let be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.
Sur la décomposition quadratique d'une suite de polynômes orthogonaux - II
Sur le diamètre transfini entier d'un intervalle réel
En utilisant à la fois la théorie des polynômes orthogonaux et des arguments élémentaires de géométrie des nombres, nous donnons ici des nouveaux encadrements pour le diamètre transfini entier d’un intervalle d’extrémités rationnelles. Ces encadrements dépendent explicitement de la longueur de et des dénominateurs de ses extrémités.