Keywords
operators
functions of bounded p-variation
absolutely p-continuous functions
Análisis funcional
operadores
funciones de p-variación acotada
funciones absolutamente p-continuas
How to Cite
Abstract
This investigation dedicates to extend the results of Gelfand regarding the abstract functions of bounded variation to the abstract functions of bounded p-variation in a sense similar to the Theorem of Representation of Riez, with the objective of applying this extension to the study of the space of the absolutely p-continuous functions. In this work the spaces of the abstract functions of strong and weak bounded p-variation in an interval are introduced and their main properties are studied. The abstract integral of Stieltjes is defined in the search of a theorem similar to that of Representation of Riesz and a representation of the continuous lineal operators of the space of the absolutely p-continuous functions on an interval in a normed weakly complete space through the abstract functions of bounded p-variation is found.
References
Gelfand, I.M. (1987) “Abstrakte Funktionen und lineare Operatoren”, en Collected Papers I, Springer Verlag, Berlin–Heidelberg–New York: 113–162.
Kisliakov, S.V. (1984) “A Remark on the space of functions of bounded p-variation”, Mathematische Nachrichten 119: 137–140.
Love, E.R.; Young, L.C. (1937) “Sur une classe de fonctionelles lineaires”, Fundamenta Mathematica 28: 110–118.
Puig de Dios, Y. (2005) Espacios de Funciones Abstractas de p-Variación Acotada Fuerte y Débil. Tesis de Licenciatura, Universidad de La Habana, Cuba.
Roldán Inguanzo, R. (1989) Raüme von Folgen und Funktionen von beschränkter p-Variation. Tesis de Doctorado, Friedrich Schiller Universität de Jena, Alemania.