https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13930 Wed 11 Apr 2018 15:55:30 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:47393 Wed 06 Mar 2024 15:04:48 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:16113 Sat 24 Mar 2018 07:55:21 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:46621 B_q of quaternionic order q, for short quaternionic B-splines, are quaternion-valued piecewise Müntz polynomials whose scalar parts interpolate the classical Schoenberg splines B_n,n ∈N, with respect to degree and smoothness. They in general do not satisfy the interpolation property B_q(n)=δ_n,0,n ∈Z. However, the application of the interpolation filter (∑_k∈ZB_qˆ(ξ+2πk))⁻¹ —if well-defined—in the frequency domain yields a cardinal fundamental spline of quaternionic order that satisfies the interpolation property. We handle the ambiguity of the quaternion-valued exponential function appearing in the denominator of the interpolation filter and relate the filter to interesting properties of a quaternionic Hurwitz zeta function and the existence of complex quaternionic inverses. Finally, we show that the cardinal fundamental splines of quaternionic order fit into the setting of Kramer’s Lemma and allow for a family of sampling, respectively, interpolation series.]]> Mon 28 Nov 2022 10:57:31 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:33802 Mon 23 Sep 2019 11:58:37 AEST ]]>