Representation and Approximation of Pseudodifferential Operators by Sums of Gabor Multipliers

Details Representation and Approximation of Pseudodifferential Operators by Sums of Gabor Multipliers Representation and Approximation of Pseudodifferential Operators by Sums of Gabor Multipliers

2009-08-14

arxiv.org/abs/0908.2051v1

Appl. Anal. 90 (2011), 385 - 401

Mathematics

Functional Analysis

16 pages

Scientific paper

We investigate a new representation of general operators by means of sums of shifted Gabor multipliers. These representations arise by studying the matrix of an operator with respect to a Gabor frame. Each shifted Gabor multiplier corresponds to a side-diagonal of this matrix. This representation is especially useful for operators whose associated matrix possesses some off-diagonal decay. In this case one can completely characterize the symbol class of the operator by the size of the symbols of the Gabor multipliers. As an application we derive approximation theorems for pseudodifferential operators in the Sjostrand class.

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