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

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090, Vienna, Austria

    Karlheinz Gröchenig & Elmar Pauwels

Authors
  1. Karlheinz Gröchenig
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  2. Elmar Pauwels
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Corresponding author

Correspondence to Elmar Pauwels.

Additional information

Communicated by D. X. Zhou.

This work was funded by the Austrian Science Fund (FWF) in project NFN SISE S106.

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Gröchenig, K., Pauwels, E. Uniqueness and reconstruction theorems for pseudodifferential operators with a bandlimited Kohn-Nirenberg symbol. Adv Comput Math 40, 49–63 (2014). https://doi.org/10.1007/s10444-013-9297-0

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  • DOI: https://doi.org/10.1007/s10444-013-9297-0

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