Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

• Autor(a) principal: Barbanti, Luciano [UNESP]
• Data de Publicação: 2012
• Outros Autores: Damasceno, Berenice Camargo [UNESP]
• Tipo de documento: Artigo de conferência
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1063/1.4765474; http://hdl.handle.net/11449/10397
• topic: Plant operator; time scales; representation of linear operators; hysteresis

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.