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arXiv · 1204.5029

Uniqueness and Reconstruction Theorems for Pseudodifferential Operators with a Bandlimited Kohn-Nirenberg Symbol

Karlheinz Gröchenig·Elmar Pauwels
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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 operators and its matrix with respect to a Gabor system.

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Karlheinz Gröchenig, Elmar Pauwels. 2012-04-23. Uniqueness and Reconstruction Theorems for Pseudodifferential Operators with a Bandlimited Kohn-Nirenberg Symbol. https://arxiv.org/abs/1204.5029

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