Basic mathematical properties of a vector Preisach operator in magnetic hysteresis modeling

This paper discusses the basic mathematical properties of the vector Preisach operator recently introduced by Delia Torre, Pinzaglia and Cardelli. This includes an investigation of isotropy with a necessary and a sufficient isotropy condition, derivation of the neutral initial state and a demagnetization process . Further, we examine the saturation behaviour with memory deletion, output alignment and a bound on the output. We show that periodic input results in periodic output and prove loop congruency. Finally, we study lag angles and losses, derive their formulas for isotropic Preisach densities and uniformly rotating input in 2 and show to be dissipative on closed loop inputs.