UNIFORM APPROXIMATION OF MULTIDIMENSIONAL MYOPIC MAPS

Our main result is a theorem that gives; in a certain setting, a neces sary and sufficient condition under which multidimensional shift-invar iant input-output maps with vector-valued inputs drawn from a certain large set can be uniformly approximated arbitrarily well using a struc ture consisting of a linear preprocessing stage followed by a memoryle ss nonlinear network. Noncausal as well as causal maps are considered, Approximations for noncausal maps for which inputs and outputs are fu nctions of more than one variable are of current interest in connectio n with, for example, image processing.