Quincunx Fundamental Refinable Functions in Arbitrary Dimensions
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 uniqu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/6/3/20 |
| _version_ | 1818999957546336256 |
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| author | Xiaosheng Zhuang |
| author_facet | Xiaosheng Zhuang |
| author_sort | Xiaosheng Zhuang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T22:25:41Z |
| format | Article |
| id | doaj.art-db4a51a1c7c04e6dbb865a512387fe51 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-20T22:25:41Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-db4a51a1c7c04e6dbb865a512387fe512022-12-21T19:24:50ZengMDPI AGAxioms2075-16802017-07-01632010.3390/axioms6030020axioms6030020Quincunx Fundamental Refinable Functions in Arbitrary DimensionsXiaosheng Zhuang0Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong KongIn 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.https://www.mdpi.com/2075-1680/6/3/20quincunx latticecheckerboard latticesum rulefull-axis symmetryinterpolatory masksinterpolatory subdivision schemesnonnegative masksfundamental refinable functions |
| spellingShingle | Xiaosheng Zhuang Quincunx Fundamental Refinable Functions in Arbitrary Dimensions Axioms quincunx lattice checkerboard lattice sum rule full-axis symmetry interpolatory masks interpolatory subdivision schemes nonnegative masks fundamental refinable functions |
| title | Quincunx Fundamental Refinable Functions in Arbitrary Dimensions |
| title_full | Quincunx Fundamental Refinable Functions in Arbitrary Dimensions |
| title_fullStr | Quincunx Fundamental Refinable Functions in Arbitrary Dimensions |
| title_full_unstemmed | Quincunx Fundamental Refinable Functions in Arbitrary Dimensions |
| title_short | Quincunx Fundamental Refinable Functions in Arbitrary Dimensions |
| title_sort | quincunx fundamental refinable functions in arbitrary dimensions |
| topic | quincunx lattice checkerboard lattice sum rule full-axis symmetry interpolatory masks interpolatory subdivision schemes nonnegative masks fundamental refinable functions |
| url | https://www.mdpi.com/2075-1680/6/3/20 |
| work_keys_str_mv | AT xiaoshengzhuang quincunxfundamentalrefinablefunctionsinarbitrarydimensions |