Orthogonal polynomials on the real line and on the unit circle.

• Grant number: 13/19551-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2014
• End date: January 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Alagacone Sri Ranga
• Grantee: Fábio Rodrigues Lucas
• 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
• Associated research grant: 09/13832-9 - Orthogonal polynomials, special functions and applications, AP.TEM

Abstract

Our interest in this projet is to look at two topics of study within the field oforthogonal polynomials. Namely, on orthogonal polynomials on the real line and on orthogonalpolynomials on the unit circle. Specifically, the topic associated with orthogonal polynomialson the real line is to find lower bonds for the zeros of certain class of polynomials. In particular,for orthogonal polynomials associated with certain discrete measures. With respect to thestudy concerning orthogonal polynomial on the unit circle, we focus on finding necessary andsufficient conditions for certain combinations of polynomials such that resulting polynomialsare orthogonal on the unit circle.