Some identities for product and degree raising of splines (Q808348)

It is shown how the algebraic product fg of two spline functions f and g, each represented in terms of B-splines, can again be represented as a linear combination of suitable B-splines. The author proves generalization of Marsden's identity and - based on this generalization - gives an explicit representation for the B-spline coefficients of a product of splines in terms of the B-spline coefficients of each factor. These results lead to simple generalizations of degree raising formulas of \textit{E. Cohen}, \textit{T. Lyche} and \textit{L. L. Schumaker} [J. Approximation Theory 46, 170-181 (1986; Zbl 0621.41009)].