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Some Results on the Space of Bounded Second Variation Functions in the Sense of Shiba
Escuela Superior Politécnica del Litoral (ESPOL), FCNM, Campus Gustavo Galindo, Guayaquil, Ecuador
Escuela Superior Politécnica del Litoral (ESPOL), FCNM, Campus Gustavo Galindo, Guayaquil, Ecuador
Escuela Superior Politécnica del Litoral (ESPOL), FCNM, Campus Gustavo Galindo, Guayaquil, Ecuador
- 1 Escuela Superior Politécnica del Litoral (ESPOL), FCNM, Campus Gustavo Galindo, Guayaquil, Ecuador
- 2 Escuela Superior Politécnica del Litoral (ESPOL), FCNM, Campus Gustavo Galindo, Guayaquil, Ecuador
- 3 Escuela Superior Politécnica del Litoral (ESPOL), FCNM, Campus Gustavo Galindo, Guayaquil, Ecuador
Advances in Pure Mathematics·Volume 10 (2020)·Pages 245–258·Published 30 April 2020·DOI10.4236/apm.2020.105015
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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.
KeywordsFunctional AnalysisBounded VariationSecond Bounded VariationBanach Space
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