Multivariate complex B-splines and Dirichlet averages

Abstract. The notion of complex B-spline is extended to a multivariate setting by means of ridge functions employing the known geometric relationship between ordinary B-splines and multivariate B-splines. To derive properties of complex B-splines in Rs, 1 < s ∈ N, the Dirichlet average has to be generalized to include infinite dimensional simplices △∞. Based on this generalization several identities of multivariate complex B-splines are presented.

• Type: Journal
• Year: 2010
• Where: JAT
• Authors: Peter Massopust, Brigitte Forster
• Keywords: B-splines, Complex B-splines, JAT 2010, Multivariate Complex B-splines