Splines and fractional differential operators

@article{Massopust2020SplinesAF,
  title={Splines and fractional differential operators},
  author={Peter R. Massopust},
  journal={International Journal of Wavelets, Multiresolution and Information Processing},
  year={2020}
}
  • P. Massopust
  • Published 31 January 2019
  • Mathematics
  • International Journal of Wavelets, Multiresolution and Information Processing
Several classes of classical cardinal B-splines can be obtained as solutions of operator equations of the form [Formula: see text] where [Formula: see text] is a linear differential operator of integral order. In this paper, 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… Expand
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Reproducing fractional monomials: Weakening of the Strang-Fix conditions
  • V. G. Zakharov
  • Computer Science, Mathematics
  • Int. J. Wavelets Multiresolution Inf. Process.
  • 2021
TLDR
The traditional relation between the degree of reproduced monomials and the order of approximation holds and bivariate, obtained by tensor product, fractional B-splines are introduced; and reproducing of bivariate causal and symmetricmonomials is shown. Expand

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