On Transforming a Tchebycheff System into a Strictly Totally Positive System

AbstractIn this paper, we give a method to transform, if possible, a Tchebycheff basis into a strictly totally positive basis. We introduce the concept of a "bicanonical" system, which is used to provide a test for whether a given Tchebycheff space has a strictly totally positive basis. We also prove that a space of functions defined on an adequate domain has a strictly totally positive basis if it has a canonical complete Tchebycheff basis or if the space is extended Tchebycheff. We also study the problem of enlarging the domain of definition of the functions in a Tchebycheff space to obtain a space with a strictly totally basis