Rational functions associated with double infinite sequences of complex numbers

[摘要] Let {mu(k)}(-infinity)(+infinity), be a given double infinite sequence of complex numbers. By defining a linear functional on the space of the Laurent polynomials, certain rational functions are first constructed and some algebraic properties studied. The hermitian case, i.e. mu(-k) = <(mu)over bar>(k), k is an element of Z is separately considered and it is shown how the theory of polynomials orthogonal on the unit circle can be used in order to prove geometric convergence for sequences such as these rational functions.

[发布日期] 1997-11-06

[关键词] Laurent polynomials;generating function;linear functional;Szego polynomials;geometric convergence