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Statistical Encounters with Complex B-Splines

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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.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Boltzmannstrasse 3, 85747, Garching, Germany

    Brigitte Forster

  2. Institute of Biomathematics and Biometry, Helmholtz Zentrum München–German Research Center for Environmental Health, Ingolstädter Landstrasse 1, 85764, Neuherberg, Germany

    Peter Massopust

Authors
  1. Brigitte Forster
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  2. Peter Massopust
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Correspondence to Peter Massopust.

Additional information

Communicated by G. Kerkyacharian.

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Forster, B., Massopust, P. Statistical Encounters with Complex B-Splines. Constr Approx 29, 325–344 (2009). https://doi.org/10.1007/s00365-008-9019-x

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  • DOI: https://doi.org/10.1007/s00365-008-9019-x

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