On Transforming a Tchebycheff System into a Strictly Totally Positive System

✍ Scribed by J.M. Carnicer; J.M. Pena

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 735 KB
• Volume: 81
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1995.1050

✦ Synopsis

In 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. 1995 Academic Press. Inc.