Expo-rational Spline Multiwavelets : a First Overview of Definitions, Properties, Generalizations and Applications

Expo-rational B-splines have been introduced in 2002 and by now have been shown to exhibit certain 'super-properties' compared to ordinary polynomial B-splines. The Euler Beta-function B-splines, a polynomial version of the expo-rational B-splines, has been introduced very recently, and has been shown to share some of the 'super-properties' of the expo-rational B-splines. In this paper we discuss several of the ways in which these 'superproperties' can be used to enhance the theory of polynomial spline wavelets and multiwavelets.