Rational functions associated with double infinite sequences of complex numbers

Let {μk}−∞+∞ 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. rmitian case, i.e. μ−k = μk, k ∈ 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.