On Regulated Functions
[ 1 ] Instytut Matematyki, Wydział Elektryczny, Politechnika Poznańska | [ P ] employee
2018
scientific article
english
- regulated functions
- discontinuous functions
- compactness
- 26A39
- 46E40
- 54C65
- 54C35
EN In this paper we investigate the space of regulated functions on a compact interval [0,1]. When equipped with the topology of uniform convergence this space is isometrically isomorphic to some space of continuous functions. We study some of its properties, including the characterization of the dual space, weak and strong compactness properties of sets. Finally, we investigate some compact and weakly compact operators on the space of regulated functions. The paper is complemented by an existence result for the Hammerstein-Stieltjes integral equation with regulated solutions.
37 - 57
CC BY-NC-ND (attribution - noncommercial - no derivatives)
publisher's website
final published version
at the time of publication
public
10
10