Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle

Abstract

This paper surveys the closely related topics included in the title. Emphasis is given to the parallelism between the approach using (Perron–Carathéodory) continued fractions to solve the trigonometric moment problem, and the alternate development that proceeds from the sequence of moments {μn}−∞∞, to the linear functional μ, to the Szegö polynomials and their reciprocal and associated polynomials, and to the quadrature formula for μ and the solution of the moment problem.