On convolutions of \(B\)-splines (Q1891034)

The main subject of this paper is the convolution of spline functions. In particular, the author gives an expression for the convolution of a spline over nonuniform knots with \(B\)-splines as a linear combination of \(B\)-splines of higher order. The coefficients are expressed in terms of divided differences and can be evaluated by a stable recurrence relation. Convolutions of multidimensional splines by tensor-product \(B\)-splines, box-splines and simplex splines are also considered.