The Green's functions theory based on a Generalized Signals & Systems Theory and its application to electromagnetics

Abstract

During the last years, a Generalized Signals and Systems Theory (GSST) is been developed by our research group. The latest version of the GSST includes important concepts concerning the generalization of the (i) study of physical systems by means of infinite dimensional signal and linear-invariant and non invariant-operator spaces; (ii) concepts associated to sets of impulse responses rigorously explained in terms of generalized infinite dimensional basis together with the theory of distributions; (iii) transformations (Generalized Transforms, GT); (iv) transformation changes-infinite dimensional basis changes-(Generalized Transform Changes, GTC) and (v) spectral analysis of systems (Generalized Spectral Analysis, GSA). All these concepts may be particularized to the Green's functions theory which is nothing more than a particular case of obtaining the integral representation — with kernel a set of impulse responses, the Green's functions — of the inverse operator of the original one usually defined by differential operators together with certain boundary conditions. This leads to try to obtain a Generalized Green's Functions Theory (GGFT) which is the final aim within the studies and results presented in this work.