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International Journal of Mathematics and Mathematical Sciences - Volume 16 1993, Issue 4, Pages 737-748

Mathematics Department, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt

Received 16 January 1992; Revised 22 June 1992

Copyright © 1993 Hindawi Publishing Corporation. 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.

Abstract

This paper presents a new complete orthonormal system of functionsdefined on the interval 0,1 and whose supports shrink to nothing. Thissystem related to the construction of the Cantor ternary set. We defined thecanonical map ξ and proved the equivalence between this system and the Walshsystem. The generalized Cantor set with any dissection ratio is establishedand the constructed system is defined in the general case.





Autor: Raafat Riad Rizkalla

Fuente: https://www.hindawi.com/



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