A Marsden type identity for periodic trigonometric splines (Q1318237)

The authors consider a partition of the plane by rays starting at the same point. The space of splines formed by \(C^{k-1}\)-functions, which are homogeneous polynomials of degree \(\leq k\) at each angular region, is investigated. An extension of Marsden's identity for periodic trigonometric splines is obtained by making use of bivariate approach to that space. A basis of these spaces, whose elements have minimal or quasi-minimal support is studied. Earlier results in this direction were obtained by W. Dahmen und C. A. Micchelli.