Interpolation by rational functions with nodes on the unit circle

From the Erdos-Turan theorem, it is known that if f is a continuous functio n on T = {z : \z\ = 1} and L-n(f, z) denotes the unique Laurent polynomial interpolating f at the (2 n + 1)th roots of unity, then [GRAPHICS] Several years later, Walsh and Sharma produced similar result but taking in to consideration a function analytic in D = {z : \z\ < 1} and continuous on bb D boolean OR T and making use of algebraic interpolating polynomials in the roots of unity. In this paper, the above results will be generalized in two directions. On the one hand, more general rational functions than polynomials or Laurent p olynomials will be used as interpolants and, on the other hand, the interpo lation points will be zeros of certain para-orthogonal functions with respe ct to a given measure on T.