Revista de la Academia Canaria de Ciencias vol:9 issue:1-2 pages:127-152
We give a brief survey to some basic elements of the theory of orthogonal rational functions. Two main cases are treated separately: I. All the poles are outside the closed unit disk, and the orthogonality measures have support in the unit circle. II. All the poles are on the extended real line, and the orthogonality measures have support in the real line. These situations generalize the theory of orthogonal polynomials on the unit circle (Szegö polynomials) and the theory of orthognal polynomials on the real line.