Some mathematical properties of a vector Preisach operator

In this paper, we present mathematical results regarding a recently introduced vectorization of the Preisach operator. The operator output can be shown to be continuous regardless of the properties of its underlying Preisach distribution. For uniaxial input originating in saturation, the output of the isotropic operator reduces to that of a scalar Preisach operator. We formulate this scalar Preisach operator explicitly and give an example for the reduction. Finally, we apply the results in order to deduce conditions under which the uniaxial scalar curves resulting from the vector Preisach operator are monotone.