Complex Box Splines

TL;DR

This paper introduces complex degree box splines, extending classical box splines, and explores their properties and connections to fractional derivatives in function spaces.

Contribution

It presents the novel concept of complex degree box splines and derives their fundamental properties and relations to fractional derivatives.

Findings

Complex degree box splines generalize classical box splines.

Properties of complex box splines are systematically derived.

Connections to fractional derivatives are established.

Abstract

The novel concept of box spline of complex degree is introduced and several of its properties derived and discussed. These box splines of complex degree generalize and extend the classical box splines. Relations to a class of fractional derivatives defined on certain function spaces are also exhibited.