Abstract
In this paper we introduce the concept of bounded variation for functions defined on compact subsets of the complex plane \(\mathbb{C}\), based on the notion of variation along a curve as defined by Ashton and Doust; We describe in detail the space so generated and show that it can be equipped, in a natural way, with the structure of a Banach algebra. We also present a necessary condition for a composition operator \(C_\varphi\) to act between two such spaces.
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