The Electromagnetic Resonant Vector and the Generalized Projection Operator

One of the current problems occurred in broadcasting processes is the lost of information that emerge for many known and unknown reasons. To avoid the lack of information we have showed a set of alternative tools some of which are indeed our proposals, but also there are other systematically used on literature like time reversal. The principal goal of the present work is to give a global instrument that help us to solve the above mentioned problems, that includes most of the referred alternatives and that specifically consist on the creation of operators we name generalized projection operators (GPO) because, having a mathematical base, also allow us to select between different procedures, that is, time reversal, information packs, etc.; another aim is to justify the use of the electromagnetic resonances as an alternative to build a convenient mathematical base that insure a minimum interference between different signals or between different projections of a signal. The methodology we follow is to recall the orthogonality properties of the electromagnetic resonant vectors and show that his properties gives to the generalized projection operators the real possibility to avoid information lacks. To this end we establish both the generalized homogeneous Fredholm equation (GHFE) and the generalized inhomogeneous equation (GIFE) for the electromagnetic fields, or for the electromagnetic vector and scalar potentials. In other works we have shown the equivalence for obtaining the resonant frequencies directly for the field or for the potential equations. From these two mentioned integral equations we obtain the orthogonality properties we need to build the GPO. Finally we give an academic example of application.