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Orthogonal Polynomials and Linear Functionals
EMS Series of Lectures in Mathematics

Juan Carlos García-Ardila (Universidad Politécnica de Madrid, Spain)
Francisco Marcellán (Universidad Carlos III de Madrid, Spain)
Misael E. Marriaga (Universidad Rey Juan Carlos, Madrid, Spain)

Orthogonal Polynomials and Linear Functionals

An Algebraic Approach and Applications

ISBN print 978-3-98547-008-2, ISBN online 978-3-98547-508-7
DOI 10.4171/ELM/33
August 2021, 128 pages, softcover, 17 x 24 cm.
39.00 Euro

This book presents an introduction to orthogonal polynomials, with an algebraic flavor, based on linear functionals defining the orthogonality and the Jacobi matrices associated with them. Basic properties of their zeros as well as quadrature rules are discussed. A key point is the analysis of those functionals satisfying Pearson equations (semiclassical case) and the hierarchy based on their class.

The book's structure reflects the fact that its content is based on a set of lectures delivered by one of the authors at the first Orthonet Summer School in Seville, Spain in 2016. The presentation of the material is self-contained and will be valuable to students and researchers interested in a novel approach to the study of orthogonal polynomials, focusing on their analytic properties.

Keywords: linear functionals, orthogonal polynomials, Jacobi matrices, zeros of orthogonal polynomials, Gauss quadrature formulas, spectral transformations, matrix factorization, semiclassical linear functionals, Askey scheme