# Quaternionic B-splines

@article{Hogan2017QuaternionicB, title={Quaternionic B-splines}, author={Jeffrey A. Hogan and Peter R. Massopust}, journal={J. Approx. Theory}, year={2017}, volume={224}, pages={43-65} }

We introduce B-splines on the line of quaternionic order $B_q$ ($q$ in the algebra of quaternions) for the purposes of multi-channel signal and image analysis. The functions $B_q$ are defined first by their Fourier transforms, then as the solutions of distributional differential equation of quaternionic order. The equivalence of these definitions requires properties of quaternionic Gamma functions and binomial expansions, both of which we investigate. The relationship between $B_q$ and a… Expand

#### 3 Citations

Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling

- Mathematics
- Complex Analysis and Operator Theory
- 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… Expand

Splines and fractional differential operators

- Mathematics
- International Journal of Wavelets, Multiresolution and Information Processing
- 2020

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… Expand

On Some Generalizations of B-Splines

- Mathematics
- 2019

In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization… Expand

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