Spline functions of negative degree

In a recent series of papers (see Goldman [1–3]), B-splines of negative degree were introduced and partially investigated. The main purpose of the present paper is to continue and to extend these investigations. In the first part, we look more deeply onto the negative degree B-splines; we present an explicit representation for them, as well as a degree elevation formula; this solves a problem posed in [3]. Moreover, in the second part we look (probably for the first time in the literature) at the structure of the space of negative degree spline functions, spanned by the negative degree B-splines. As a main result here, we obtain a truncated power function representation of these splines. Received: May 1999 / Accepted: November 1999