On translation invariant operators which preserve the B-spline recurrence

It was observed in [4] that the Hilbert transform of the univariate B-spline preserves the B-spline recurrence. Motivated by this observation, we characterize translation invariant operators that preserve the multivariate B-spline recurrence and analogous results are also provided for the multivariate cube spline. Key words. Multivariate B-spline recurrence, cube splines, translation invariant operators, homogeneous distributions. AMS subject classifications. 41A15, 44A35

• Type: Journal
• Year: 2008
• Where: ADCM
• Authors: Charles A. Micchelli, Yuesheng Xu, Haizhang Zhang
• Keywords: ADCM 2008, B-spline Recurrence, Multivariate B-spline Recurrence, Translation Invariant Operators