On the representation of hysteresis operators of Preisach type

Abstract

Brokate and Sprekels introduced the notion of hysteresis operators of the Preisach type (HOPTs), that are more general than (and include as a subset) the classical Preisach operator. In this paper, we provide a mathematical framework to the important representation problem for HOPTs by presenting two results on the approximation of the output function on the set of memory curves. One of the results shows the existence of a neural network representation when the functional is continuous, and the other shows a representation based on a multiresolution analysis when the functional is Hölder continuous and bounded on compact subsets of the space of memory curves.