https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:54550 Tue 27 Feb 2024 20:46:44 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:34607 Tue 02 Apr 2019 16:42:14 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:32073 B_q of quaternionic order q, defined on the real line for the purposes of multi-channel signal analysis. The functions B_q are defined first by their Fourier transforms, then as the solutions of a 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 backwards difference operator is shown, leading to a recurrence formula. We show that the collection of integer shifts of B_q is a Riesz basis for its span, hence generating a multiresolution analysis. Finally, we demonstrate the pointwise and L^p convergence of the quaternionic B-splines to quaternionic Gaussian functions.]]> Fri 27 Apr 2018 11:52:51 AEST ]]>