International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 737-748
An orthonormal system on the construction of the generalized cantor set
Mathematics Department, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt
Received 16 January 1992; Revised 22 June 1992
Copyright © 1993 Raafat Riad Rizkalla. 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.
This paper presents a new complete orthonormal system of functions
defined on the interval and whose supports shrink to nothing. This
system related to the construction of the Cantor ternary set. We defined the
canonical 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.