Orthogonal and similar polynomials: properties and applications

• Grant number: 10/12783-1
• Support Opportunities: Regular Research Grants
• Start date: October 01, 2010
• End date: September 30, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alagacone Sri Ranga
• Grantee: Alagacone Sri Ranga
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• City of the host institution: São José do Rio Preto
• Associated researchers: Regina Litz Lamblim

Abstract

The theory of orthgonal polynomials has vast applications in all types of problems of Mathematics and Applied Sciences. These polynomials are essentials tools for the solutions of many problems and have contributed in studies related to Differential equations, Continued fractions, Numerical stability, Fast and super-fast algorithms, etc. Our recent involvement in this area of research involve studies of 1) Orthogonal polynomials on the real line, 2) Szegö polynomials which are given interms of integrals on the unit circle, 3) Orthogonal Laurent polynomials that require also negative moments and 4) Sobolev orthogonal polynomials defined interm of inner products involving derivatives. (AU)