Multivariate complex B-splines and Dirichlet averages

Peter Massopust, Brigitte Forster

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The notion of a 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 Δ. Based on this generalization several identities of multivariate complex B-splines are presented.

Original languageEnglish
Pages (from-to)252-269
Number of pages18
JournalJournal of Approximation Theory
Issue number2
StatePublished - Feb 2010


  • Complex splines
  • Dirichlet average
  • Multivariate splines
  • Weyl fractional derivative and integral


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