Marsdenʹs identity Original Research Article

This paper consists of two parts. In the first part, a short new proof of Marsdenʹs identity is given. It is shown that this identity is equivalent to the blossoming theorem, to a formula for rational linear transformation of B-splines (and later, to the B-spline recurrence relations). In the second part, we develop the basic univariate spline theory entirely from Marsdenʹs identity (or rather, a preliminary form of it), without resorting to the divided difference machinery.