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Constructive Approximation

, Volume 29, Issue 3, pp 325–344 | Cite as

Statistical Encounters with Complex B-Splines

  • Brigitte Forster
  • Peter MassopustEmail author
Article

Abstract

Complex B-splines as introduced in Forster et al. (Appl. Comput. Harmon. Anal. 20:281–282, 2006) are an extension of Schoenberg’s cardinal splines to include complex orders. We exhibit relationships between these complex B-splines and the complex analogues of the classical difference and divided difference operators and prove a generalization of the Hermite–Genocchi formula. This generalized Hermite–Genocchi formula then gives rise to a more general class of complex B-splines that allows for some interesting stochastic interpretations.

Keywords

Complex B-splines Divided differences Weyl fractional derivative and integral Hermite–Genocchi formula Dirichlet mean Submartingale Poisson–Dirichlet process GEM distribution 

Mathematics Subject Classification (2000)

41A15 60E05 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität MünchenGarchingGermany
  2. 2.Institute of Biomathematics and BiometryHelmholtz Zentrum München–German Research Center for Environmental HealthNeuherbergGermany

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