A First Course on Orthogonal Polynomials

This book provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials.

A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials, which distinguishes it from other contributions in the field.

Features

• Suitable for a graduate course in orthogonal polynomials
• Can be used for a short course on the algebraic theory of orthogonal polynomials and its applicability to the study of the "old" classical orthogonal polynomials
• Includes numerous exercises for each topic

• Real and complex analysis are the only prerequisites

  Autorentext

  Kenier Castillo is currently the FCT Assistant Researcher at Centre for Mathematics of the University of Coimbra (Portugal). He earned his doctorate from Carlos III University of Madrid (Spain) in 2012. His research interests include Special Functions and Orthogonal Polynomials. He has more than 50 papers in peer-review journals. Castillo supervised two doctoral theses, one at the University of Coimbra and the other at the University of Cádiz (Spain), and currently supervises two PhD students at the University of Coimbra.

  José Carlos Petronilho was an Associate Professor with Aggregation at the Department of Mathematics at the University of Coimbra. He earned his doctorate from the University of Coimbra in 1997. His research interests included Special Functions and Orthogonal Polynomials. He authored more than 40 papers in peer-review journals. In June 2024, a conference entitled "From Classical to Modern Analysis" within the framework of the European Congress of Mathematics was held to honor the memory of José Carlos Petronilho.

  Inhalt

  1. Foundations of the algebraic theory. 2. Orthogonal polynomial sequences. 3. Zeros and Gauss-Jacobi mechanical quadrature. 4. The spectral theorem. 5. The Markov theorem. 6. Orthogonal polynomials and dual basis. 7. Functional differential equation. 8. Classical orthogonal polynomials: General properties. 9. Functional equation on lattices. 10. Classical orthogonal polynomials: The positive definite case. 11. Hypergeometric series. A. Locally Convex Spaces.