Chain sequences and compact perturbations of orthogonal polynomials.
Characteristic functions and -orthogonality properties of Chebyshev polynomials of third and fourth kind.
Classical 2-orthogonal polynomials and differential equations.
Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials
In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them. We derive expressions of generalized Legendre polynomials and generalized ultraspherical polynomials by means of classical Jacobi polynomials.
Compact Jacobi matrices : from Stieltjes to Krein and
Complex and distributional weights for sieved ultraspherical polynomials.
Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas....
Constructive function theory and spline systems
Continuous symmetrized Sobolev inner products of order . II.
Costruzione di un sistema di polinomi ortonormali a partire da due suoi polinomi consecutivi
The following result is proved: to give two consecutive polynomials , of an orthonormal system is equivalent to assign the first moments of the Lebesgue-Stieltjes measure associated with the system.
Counting peaks and valleys in a partition of a set.