Biorthogonal systems to rational functions

Abstract. In this paper we start from a given rational function system and take the linear space spanned by it. Then in this linear space we construct a rational function system that is biorthogonal to the original one. By means of biorthogonality expansions in terms of the original rational functions can be easily given. For the discrete version we need to choose the points of discretization and the weight function in the discrete scalar product in a proper way. Then we obtain that the biorthogonality relation holds true for the discretized systems as well.