A Favard theorem for rational functions (Q2640725)

Let \({\mathcal R}\) be the set of rational functions whose poles are contained in a fixed, finite subset of the complex plane. Let \(\{Q_ n\}\) be a monic regular sequence of elements in \({\mathcal R}\). It is shownthat \(\{Q_ n\}\) is an orthogonal sequence with respect to a linear functional on \({\mathcal R}\) if and only if the \(Q_ n\) satisfy a certain set of three term recurrence relations. The connection with multipoint Padé continued fractions and multipoint Padé approximants (with a finite set of interpolation knots) is expressed.