Geodesic
Functions of bounded variations on compact subsets of \(\mathbb{C}\)
Commentationes Mathematicae, Tome 54 (2014) no. 1, pp. 3-19.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/cm.v54i1.757
Classification : 26A45, 47B33
Mots-clés : Functions of bounded variation, variation along a curve, composition operator 
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Jose Gimenez; Nelson Merentes; Miguel Vivas. Functions of bounded variations on compact subsets of \(\mathbb{C}\). Commentationes Mathematicae, Tome 54 (2014) no. 1, pp.  3-19. doi : 10.14708/cm.v54i1.757. http://geodesic.mathdoc.fr/articles/10.14708/cm.v54i1.757/

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