The Spectral Theory of Toeplitz Operators. (AM-99) (Annals of Mathematics Studies)

L. Boutet de Monvel , Victor Guillemin

ISBN 10: 0691082790 / ISBN 13: 9780691082790

Published by Princeton University Press, 1981

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Bibliographic Details

Title: The Spectral Theory of Toeplitz Operators. (...

Publisher: Princeton University Press

Publication Date: 1981

Binding: Soft cover

Condition: Very Good

About this title

Synopsis:

The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations.



If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol.



It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.