Differential Algebra, Complex Analysis and Orthogonal Polynomials
About this Title
Primitivo B. Acosta-Humánez and Francisco Marcellán, Editors
This volume represents the 2007–2008 Jairo Charris Seminar in Algebra and Analysis on Differential Algebra, Complex Analysis and Orthogonal Polynomials, which was held at the Universidad Sergio Arboleda in Bogotá, Colombia.
It provides the state of the art in the theory of Integrable Dynamical Systems based on such approaches as Differential Galois Theory and Lie Groups as well as some recent developments in the theory of multivariable and $q$-orthogonal polynomials, weak Hilbert's 16th Problem, Singularity Theory, Tournaments in flag manifolds, and spaces of bounded analytic functions on the unit circle.
The reader will also find survey presentations, an account of recent developments, and the exposition of new trends in the areas of Differential Galois Theory, Integrable Dynamical Systems, Orthogonal Polynomials and Special Functions, and Bloch–Bergman classes of analytic functions from a theoretical and an applied perspective.
The contributions present new results and methods, as well as applications and open problems, to foster interest in research in these areas.
Graduate students and research mathematicians interested in orthogonal polynomials, differential algebra, and integrability of dynamical systems.
Table of Contents
- David Blázquez-Sanz and Juan José Morales-Ruiz – Differential Galois theory of algebraic Lie-Vessiot systems [MR 2647636]
- Lidia Fernández, Francisco Marcellán, Teresa E. Pérez and Miguel A. Piñar – Recent trends on two variable orthogonal polynomials [MR 2647637]
- Cesar A. Gomez S. – On the integrability of the Riccati equation [MR 2647638]
- Mourad E. H. Ismail – Two discrete systems of $q$-orthogonal polynomials [MR 2647639]
- J. Ławrynowicz, L. F. Reséndis O. and L. M. Tovar S. – Like-hyperbolic Bloch-Bergman classes [MR 2647640]
- J. Tomás Lázaro – Some words about the application of Tchebycheff systems to weak Hilbert’s 16th problem [MR 2647641]
- David Mond – From the index of a differential operator to the Milnor number of a singularity [MR 2647642]
- Juan J. Morales-Ruiz and Jean-Pierre Ramis – Integrability of dynamical systems through differential Galois theory: a practical guide [MR 2647643]
- Marlio Paredes and Sofía Pinzón – Tournaments and parabolic almost complex structures on flag manifolds [MR 2647644]