Orthogonal Polynomials

The origins of the theory of orthogonal polynomials go back at least to the 18th century when they were studied in terms of continued fractions. The theory is now large and complex: a crossroad of several important domains of analysis such as analytic function theory, analytic theory of differential equations, Fourier and harmonic analysis, spectral theory of Sturm-Liouville operators, and approximation and interpolation, among others.