Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling

@article{Hogan2019QuaternionicFC,
  title={Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling},
  author={Jeffrey A. Hogan and Peter R. Massopust},
  journal={Complex Analysis and Operator Theory},
  year={2019}
}
B-splines $B_{q}$, $\Sc q > 1$, of quaternionic order $q$, for short quaternionic B-splines, are quaternion-valued piecewise M\"{u}ntz polynomials whose scalar parts interpolate the classical Schoenberg splines $B_{n}$, $n\in\N$, with respect to degree and smoothness. As the Schoenberg splines of order $\geq 3$, they in general do not satisfy the interpolation property $B_{q}(n-k) = \delta_{n,k}$, $n,k\in\Z$. However, the application of the interpolation filter $1/\sum\limits_{k\in\Z} \widehat… Expand

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