Statistical Encounters with Complex B-Splines
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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.
KeywordsComplex 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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