Special functions of mathematical physics, and among them orthogonal polynomials, have been and still are an important research subject of mathematics, both pure and applied. Their applications go from probability to quantum mechanics including number theory. Orthogonal polynomials are nowadays in Italy and Spain a very active research area with an excellent international projection.

The aim of this special session is to show some recent trends on this topic at international level. In the last years, an intensive activity was focused on the study of analytic properties of orthogonal polynomials with respect to several patterns of inner products: Sobolev inner products defined by a vector of measures, inner products defined by matrices of measures, inner products defined by measures supported on the unit circle and so on. The asymptotic behavior of these polynomials and the location of their zeros, as well as the spectral analysis of differential/difference operators such that those polynomials are eigenfunctions have attracted the interest of many researchers. Their applications to integrable systems (in particular in the analysis of the Toda hierarchy and the supersymmetry SUSY models), factorization of some structured matrices (Jacobi and CMV) and differential operators (Darboux transformations, bispectrality), Fourier analysis and the connections with numerical methods for boundary value problems have been also studied in such a way that we have an interdisciplinary approach where many branches of mathematics are very useful.

• Antonio J. Durán (University of Sevilla, Spain) - duran@us.es
• Francisco Marcellán (Charles III University of Madrid, Spain)
• Donatella Occorsio (University of Basilicata, Italy)
• Maria Grazia Russo (University of Basilicata, Italy)

Below you can download the schedule and the abstracts of all talks of this special session.

• Carlos Álvarez Fernández (Comillas Pontifical University, Spain)

           An algebraic approach to the calculation of Christoffel-Darboux formulas and recursion relations under a generalized Hankel symmetry

• Mirella Cappelleti Montano (University of Bari, Italy)

          Asymptotic formulae for Bernstein-Schnabl operators associated to a Markov operator

• Roberto Cavoretto (University of Turin, Italy)

          Numerical algorithms for multivariate approximation in convex domains

• Francesco Dell'Accio (University of Calabria, Italy)

          Hermite-Birkhoff interpolation of scattered data by combined Shepard operators

• Filomena Di Tommaso (University of Calabria, Italy)

          Multinode inverse distance methods for function approximation

• Edmundo Huertas Cejudo (University of Coimbra, Portugal)

           Algorithmic approach to the strong and ratio asymptotic expansions for Laguerre polynomials

• Erik Koelink (Radboud University Nijmegen, Netherlands)

           Matrix-valued Gegenbauer polynomials

• Vita Leonessa (University of Basilicata, Italy)

           Approximation and shape preserving properties for Bernstein-Schnabl operators associated with Markov operators

• Mariarosa Mazza (University of Insubria, Italy)

           On the constrained mock-Chebyshev least-squares

• Ester Pérez Sinusia (University of Zaragoza, Spain)

           Convergent and asymptotic expansions of solutions of second-order differential equations with a large parameter

• Maria Francisca Pérez Valero (Charles III University of Madrid, Spain)

           On asymptotics of partial derivatives of diagonal Laguerre kernels and some applications to Sobolev orthogonal polynomials

• Darío Ramos López (University of Almería, Spain)

           Comparison of two schemes for computing the diffraction integral of an optical system

• Vanesa Sánchez Canales (University of Sevilla, Spain)

           Discrete Rodrigues' formulas for orthogonal matrix polynomials satisfying second-order difference equations

• Gabriele Santin (University of Padua, Italy)

           Bases for Radial Basis Function approximation