Splines and Fractional Differential Operators
Functional Analysis
2019-02-01 v1
Abstract
Several classes of classical cardinal B-splines can be obtained as solutions of operator equations of the form where is a linear differential operator of integral order. (Cf., for instance, \cite{akhiezer,Golomb,Krein,micchelli,schoenberg}.) In this article, we consider classes of generalized B-splines consisting of cardinal polynomial B-splines of complex and hypercomplex orders and cardinal exponential B-splines of complex order, and derive the fractional linear differential operators that are naturally associated with them. For this purpose, we also present the spaces of distributions onto which these fractional differential operators act.
Cite
@article{arxiv.1901.11304,
title = {Splines and Fractional Differential Operators},
author = {Peter Massopust},
journal= {arXiv preprint arXiv:1901.11304},
year = {2019}
}