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. Laurençot 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.
Cauchy-Stieltjes integral on time scales in banach spaces and hysteresis operators
9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012 ; 2012 ; Vienna, Austria
AIP Conference Proceedings ; 1493 , 1 ; 88-90
06.11.2012
3 pages
Aufsatz (Konferenz)
Elektronische Ressource
Englisch
Cauchy-Stieltjes integral on time scales in banach spaces and hysteresis operators
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