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 To...

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Bibliographic Details

Main Authors:	Boutet de Monvel, Louis 1941-2014 (Author), Guillemin, Victor 1937- (Author)
Format:	Electronic eBook
Language:	English
Published:	Princeton, NJ Princeton University Press [1981]
Series:	Annals of Mathematics Studies number 99
Subjects:	Spectral theory (Mathematics) Toeplitz operators Spektraltheorie Toeplitz-Operator
Online Access:	Volltext
Summary:	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
Item Description:	Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016)
Physical Description:	1 online resource
ISBN:	9781400881444
DOI:	10.1515/9781400881444