Uniqueness and Reconstruction Theorems for Pseudodifferential Operators   with a Bandlimited Kohn-Nirenberg Symbol
  Motivated by the problem of channel estimation in wireless communications, we derive a reconstruction formula for pseudodifferential operators with a bandlimited symbol. This reconstruction formula uses the diagonal entries of the matrix of the pseudodifferential operator with respect to a Gabor system. In addition, we prove several other uniqueness theorems that shed light on the relation between a pseudodifferential operators and its matrix with respect to a Gabor system. 
Karlheinz Gr\"ochenig, Elmar Pauwels
math.FA