ORTHOGONAL RATIONAL FUNCTIONS ON THE UNIT CIRCLE

In this paper, we introduce the theory of orthogonal rational functions (ORFs) on the unit circle, for a measure that is supported on the unit circle of the complex plane, and compute the coefficients of the recurrence relation of these functions. Also, we shall be concerned with the problem of approximating the integral I¹ffg = R ¼ ¡¼ f(eiµ)d¹(µ) by means of the formula Inffg = Pn j=1 A(n) j f(x(n) j ), where ¹ is some finite positive measure.