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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| Main Author: | |
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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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |