International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 737-748
doi:10.1155/S0161171293000924
An orthonormal system on the construction of the generalized Cantor set
Raafat Riad Rizkalla
Mathematics Department, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt
Abstract
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.