Beyond Volterra and Wiener: some new results and open problems in nonlinear circuits and systems

New developments in nonlinear dynamical systems are permitting Volterra and Wiener nonlinear functional series representations to be optimally approximated by artificial neural networks, which are capable of adaptation, learning and evoluation by training. The enabling framework developed by the author based on a Generalized Fock Space is described. In particular, the realization of a best approximation to Wiener´s Laguerre/Hermite representation in terms of a dynamical functional artificial neural network (D-FANN) is presented. Possible impact on new technologies is discussed