Bases in banach spaces of smooth functions on cantor-type sets

Abstract

We construct Schauder bases in the spaces of continuous functions C p (K) and in the Whitney spaces E p (K) where K is a Cantor-type set. Here different Cantortype sets are considered. In the construction, local Taylor expansions of functions are used. Also we show that the Schauder basis which we constructed in the space Cp(K), is conditional.