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Axioms 2017, 6(3), 20; doi:10.3390/axioms6030020

Quincunx Fundamental Refinable Functions in Arbitrary Dimensions

Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong
Academic Editor: Palle E. T. Jorgensen
Received: 16 June 2017 / Revised: 3 July 2017 / Accepted: 4 July 2017 / Published: 6 July 2017
(This article belongs to the Special Issue Wavelet and Frame Constructions, with Applications)
View Full-Text   |   Download PDF [805 KB, uploaded 10 July 2017]

Abstract

In this paper, we generalize the family of Deslauriers–Dubuc’s interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in arbitrary dimensions. We show that a family of unique quincunx interpolatory masks exists and such a family of masks is of real value and has the full-axis symmetry property. In dimension d = 2 , we give the explicit form of such unique quincunx interpolatory masks, which implies the nonnegativity property of such a family of masks. View Full-Text
Keywords: quincunx lattice; checkerboard lattice; sum rule; full-axis symmetry; interpolatory masks; interpolatory subdivision schemes; nonnegative masks; fundamental refinable functions quincunx lattice; checkerboard lattice; sum rule; full-axis symmetry; interpolatory masks; interpolatory subdivision schemes; nonnegative masks; fundamental refinable functions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zhuang, X. Quincunx Fundamental Refinable Functions in Arbitrary Dimensions. Axioms 2017, 6, 20.

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