An orthonormal system on the construction of the generalized cantor set - Raafat Riad Rizkalla (International Journal of Mathematics and Mathematical Sciences)
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.