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The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganés, Spain, from July 3 to July 6, 2018. These meetings were mainly focused to encourage research in the fields of approximation theory, special functions, orthogonal polynomials and their applications among graduate students as well as young researchers from Latin America, Spain and Portugal. The presentation of the state of the art as well as some recent trends constitute the aim of the lectures delivered in the EIBPOA by worldwide recognized researchers in the above fields. In this volume, several topics on the theory of polynomials orthogonal with respect to different inner products are analyzed, both from an introductory point of view for a wide spectrum of readers without an expertise in the area, as well as the emphasis on their applications in topics as integrable systems, random matrices, numerical methods in differential and partial differential equations, coding theory, and signal theory, among others.

Mathematical analysis. --- Analysis (Mathematics). --- Special functions. --- Difference equations. --- Functional equations. --- Approximation theory. --- Functions of complex variables. --- Fourier analysis. --- Analysis. --- Special Functions. --- Difference and Functional Equations. --- Approximations and Expansions. --- Functions of a Complex Variable. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Equations, Functional --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Special functions --- 517.1 Mathematical analysis --- Orthogonal polynomials --- Fourier analysis --- Functions, Orthogonal