Local sampling and approximation of operators with bandlimited Kohn-Nirenberg symbols (Q485321)

The aim of the present paper is to develop discrete representations of operators with bandlimited Kohn-Nirenberg symbols that, on the one hand, can be computed in a direct and simple way from the output corresponding to a test signal and, on the other hand, have locality properties analogous to those we appreciate in the classical sampling theory. The authors show that, in order to recover a bandlimited operator precisely, the identifier cannot decay in time or in frequency. Also, in order to obtain a local approximation of an operator, it is sufficient to test the operator on a compactly supported Schwarz class function.