Orthogonal polynomials on the unit circle

• Grant number: 13/12576-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2013
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Vanessa Gonçalves Paschoa Ferraz
• Grantee: Charles Ferreira dos Santos
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil

Abstract

There is a wide range on mathematics related to the topic orthogonal polynomials, so the development of this project helps getting a deeper knowledge of key areas of mathematics. The topic orthogonal polynomials on the unit circle treats variables in the complex plane and not just reals as the orthogonal polynomials of the real line, in this way allows us to explore concepts related to complex variables. The main objective of this project is the study of orthogonal polynomials on the unit circle, their properties and relations with orthogonal polynomials on the real line. Three topics related to these polynomials are proposed in this project: quadrature formulas for functions of a complex variable, the moments problem and extreme properties. Another aspect involved in the choice of the theme is the interest for the area of analysis and the excellent academic performance of the student that demonstrates maturity for this topic.