A TAUBERIAN THEOREM FOR SERIES OF ORTHOGONAL RATIONAL FUNCTIONS

摘要

The so-called Takenaka-Malmquist system consists of a sequence of functions obtained from the sequence of rational fractions by applying the Gram-Schmidt orthogonalization procedure with respect to the Lesbegue measure on the unite circle. A Tauberian theorem for series with respect to the Takenaka-Malmquist system is proved.