THE SPECTRAL THEORY OF TOEPLITZ OPERATORS. (AM-99), VOLUME 99 by Louis Boutet de Monvel, Victor Guillemin ( 9780691082790 )

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Title:

THE SPECTRAL THEORY OF TOEPLITZ OPERATORS. (AM-99), VOLUME 99

By:

Louis Boutet de Monvel, Victor Guillemin

Format:

Paperback

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ISBN 10:

0691082790

ISBN 13:

9780691082790

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Publisher:

PRINCETON UNIVERSITY PRESS

Pub. date:

1 August, 1981

Series:

Annals of Mathematics Studies 99

Pages:

166

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.

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Imprint:

Princeton University Press

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Returnable

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