Volterra Differential Constitutive Operators and Locality Considerations in Electromagnetic Theory - Abstract

equations. This infrastructure requires the supplement of constitutive equations. Recently a general framework has been suggested, taking into account dispersion, inhomogeneity and nonlinearity, in which the constitutive equations are posited as dierential equations involving the dierential operators based on the Volterra functional series. The validity of such representations needs to be examined. Here it is shown that for such representations to be eective, the spatiotemporal functions associated with the Volterra dierential operators must be highly localized, or equivalently, widely extended in the transform space. This is achieved by exploiting Delta-function expansions, leading in a natural way to polynomial dierential operators. The Four-vector Minkowski space is used throughout, facilitating general results and compact notation.