On Economization of Rational Functions

Rational functions with real poles and poles in the complex lower half-plane, orthogonal on the real line, are well known. Quadrature formulas similar to the Gauss formulas for orthogonal polynomials have been studied. We generalize to the case of ...

In this paper we present formulas expressing the orthogonal rational functions associated with a rational modification of a positive bounded Borel measure on the unit circle, in terms of the orthogonal rational functions associated with the initial ...

Let A={α₁, α₂...} be a sequence of numbers on the extended real line R^{^}=R∪{∞} and µ a positive bounded Borel measure with support in (a subset of) R^{^}. We introduce rational functions φ_n with poles {α₁,...α_n} that are orthogonal with respect to µ (if all ...