An orthonormal system on the construction of the generalized cantor set
This paper presents a new complete orthonormal system of functions defined on the interval [0,1] and whose supports shrink to nothing. This system related to the construction of the Cantor ternary set. We defined the canonical map ξ and proved the equivalence between this system and the Walsh system...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000924 |
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| _version_ | 1832553255671955456 |
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| author | Raafat Riad Rizkalla |
| author_facet | Raafat Riad Rizkalla |
| author_sort | Raafat Riad Rizkalla |
| collection | DOAJ |
| description | This paper presents a new complete orthonormal system of functions
defined on the interval [0,1] and whose supports shrink to nothing. This
system related to the construction of the Cantor ternary set. We defined the
canonical map ξ and proved the equivalence between this system and the Walsh
system. The generalized Cantor set with any dissection ratio is established
and the constructed system is defined in the general case. |
| format | Article |
| id | doaj-art-51e32765f37c487daa330258e7304da0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-51e32765f37c487daa330258e7304da02025-02-03T05:54:23ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116473774810.1155/S0161171293000924An orthonormal system on the construction of the generalized cantor setRaafat Riad Rizkalla0Mathematics Department, Faculty of Education, Ain Shams University, Heliopolis, Cairo, EgyptThis paper presents a new complete orthonormal system of functions defined on the interval [0,1] and whose supports shrink to nothing. This system related to the construction of the Cantor ternary set. We defined the canonical map ξ and proved the equivalence between this system and the Walsh system. The generalized Cantor set with any dissection ratio is established and the constructed system is defined in the general case.http://dx.doi.org/10.1155/S0161171293000924dyadic expansionWalsh functionsCantor set. |
| spellingShingle | Raafat Riad Rizkalla An orthonormal system on the construction of the generalized cantor set International Journal of Mathematics and Mathematical Sciences dyadic expansion Walsh functions Cantor set. |
| title | An orthonormal system on the construction of the generalized cantor set |
| title_full | An orthonormal system on the construction of the generalized cantor set |
| title_fullStr | An orthonormal system on the construction of the generalized cantor set |
| title_full_unstemmed | An orthonormal system on the construction of the generalized cantor set |
| title_short | An orthonormal system on the construction of the generalized cantor set |
| title_sort | orthonormal system on the construction of the generalized cantor set |
| topic | dyadic expansion Walsh functions Cantor set. |
| url | http://dx.doi.org/10.1155/S0161171293000924 |
| work_keys_str_mv | AT raafatriadrizkalla anorthonormalsystemontheconstructionofthegeneralizedcantorset AT raafatriadrizkalla orthonormalsystemontheconstructionofthegeneralizedcantorset |