TITLE:
Some Results on the Space of Bounded Second Variation Functions in the Sense of Shiba
AUTHORS:
Liliana Pérez, Ebner Pineda, Luz Rodríguez
KEYWORDS:
Functional Analysis, Bounded Variation, Second Bounded Variation, Banach Space
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.10 No.5,
May
12,
2020
ABSTRACT: In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba; an integral representation theorem is also proved and necessary conditions are given for that the space be closed under composition of functions. Another significant result is the proof that this space of bounded second variation in the sense of Shiba is a Banach algebra, which is not immediate as it happens in other spaces of generalized bounded variation.