Null spaces of differential operators, polar forms, and splines (Q1919086)

In this paper, the authors consider a very general class of so-called \({\mathcal D}\)-polynomials based on the solution of an initial value problem for certain constant coefficient second order differential operators. Based on a general theory of polar forms, a Bernstein-Bézier approach for such \({\mathcal D}\)-polynomials is described, and subsequently a spline theory for piecewise \({\mathcal D}\)-polynomials which includes known approaches such as algebraic and trigonometric polynomial splines and hyperbolic splines. Specifically, knot insertion and subdivision are investigated in this general context.