Interpolation Methods for the Evaluation of 2π-Periodic Finite Baire Measure

We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on -π,π]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L ^p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2π-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures.