Dirichlet splines as fractional integrals of \(B\)-splines
type: Item
instance of: scholarly article
title: Dirichlet splines as fractional integrals of \(B\)-splines
zbMATH Open document ID: 1032.41005
published in: Rocky Mountain Journal of Mathematics
publication date: 2003-12-03T00:00:00Z
full work available at URL: CONT32-2.html
review text: The definition of a divided difference is generalized to divided differences with a continuous parameter in \(\mathbb R^{k+1}_+\). The special case when the parameter's components are integral corresponds to divided differences with multiple knots. For this, so-called Dirichlet averages are used. A relation to \(B\)-splines via fractional derivatives is established too.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 62H10
zbMATH DE Number: 2012107
zbMATH Keywords: Dirichlet averages
zbMATH Keywords: Dirichlet splines
zbMATH Keywords: divided differences
zbMATH Keywords: B-splines
zbMATH Keywords: Dirichlet distribution
zbMATH Keywords: fractional integrals
zbMATH Keywords: fractional derivatives
author: Wolfgang zu Castell
reviewed by: Martin D. Buhmann
MaRDI profile type: Publication
OpenAlex ID: W1977149119
cites work: l-1 summability of multiple Fourier integrals and positivity
cites work: On alpha-symmetric multivariate distributions
cites work: Lauricella's hypergeometric function \(F_ D\)
cites work: A Connection Between Elementary Functions and Higher Transcendental Functions
cites work: Q4175520
cites work: \(B\)-splines, hypergeometric functions, Dirichlet averages
cites work: Q4723000
cites work: Q4103811
cites work: Q5553606
cites work: Multivariate splines: a probabilistic perspective
cites work: Generalized Liouville differentiation and the method of multipliers in the theory of imbeddings of classes of differentiable functions
cites work: A constructive approach to Kergin interpolation in \(R^ k\): Multivariate B-splines and Lagrange interpolation
cites work: Moments of Dirichlet splines and their applications to hypergeometric functions
cites work: Q4772680
cites work: Inversion theorems for poterntial-type integral transforms in a and onsn-1
DOI: 10.1216/RMJM/1030539686
description: scientific article; zbMATH DE number 2012107