Uniqueness and reconstruction theorems for pseudodifferential operators with a bandlimited Kohn-Nirenberg symbol

Authors:
Karlheinz Gröchenig;Elmar Pauwels
Affiliations:
Faculty of Mathematics, University of Vienna, Vienna, Austria 1090;Faculty of Mathematics, University of Vienna, Vienna, Austria 1090
Venue:
Advances in Computational Mathematics
Year:
2014

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Abstract

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 operator and its matrix with respect to a Gabor system.