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A model for Toeplitz operators in the space of entire functions of exponential type. (English) Zbl 0798.47019
This author studies Toeplitz type operators associated to pseudodifferential operators. He uses wave packets and a push-forward to build a model for such operators. A notion of “total symbol” for these operators is defined. The author proves that operators having nonnegative symbols are positive. This result is used to deduce sharp Gårding type inequalities.

MSC:
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47G30 Pseudodifferential operators
32A15 Entire functions of several complex variables
35S99 Pseudodifferential operators and other generalizations of partial differential operators
44A10 Laplace transform
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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References:
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