Exponential box splines
The exponential box splines for a set of n directions in \(Z^ s\) and for a vector of constants \(\lambda \in R^ n\) are constructed. Basic properties of these splines are derived, e.g. that they have the same smoothness and support as the polynomial box splines, and that they are positive piecewise exponential in their supports. The recurrence relations for the exponential box splines turn out to be simpler than those for the polynomial case. The author classifies the various types of exponential box splines obtained for different choices of \(\lambda\) 's. The simple box splines are defined and their corresponding \(\lambda\) 's are shown to constitute an open and dense set in \(R^ n\). A typical example of the usefulness of these splines is shown.
scientific article; zbMATH DE number 4103662
scientific article