Titlebook: Orthogonal Polynomials; Theory and Practice Paul Nevai Book 1990 Kluwer Academic Publishers 1990 Approximation.Jacobi.boundary element meth

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An Introduction to Group Representations and Orthogonal Polynomials,ions for the rotation groups in Euclidean space (ultraspherical polynomials), and the matrix elements of .(2) (Jacobi polynomials) are discussed. A general theory for finite groups acting on graphs, giving a finite set of discrete orthogonal polynomials is given. Explicit examples include graphs giving the Krawtchouk and Hahn polynomials.

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Orthogonal Polynomials978-94-009-0501-6Series ISSN 1389-2185

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Characterization Theorems for Orthogonal Polynomials,We survey in this paper characterization theorems dealing with polynomial sets which are orthogonal on the real line.

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Orthogonal Polynomials and Functional Analysis,This paper studies the measure of orthogonality for a system of polynomials defined by a three term recursion formula, using the techniques of operator theory and functional analysis. Spectral properties of self-adjoint operators and compact operators, perturbation theorems, and commutator equations are used in the development of the ideas.

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Orthogonal Polynomials Associated with Root Systems,The orthogonal polynomials that are the subject of these lectures are Laurent polynomials in several variables. They depend rationally on two parameters q and t, and there is a family of them attached to each root system R. For particular values of the parameters q and t, these polynomials reduce to objects familiar in representation theory: