The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 /

The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / / Victor Guillemin, L. Boutet de Monvel.

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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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Boutet de Monvel, L.,
Guillemin, Victor,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1981
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 99
Online Access:
Physical Description:1 online resource (166 p.)
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100 1 |a Boutet de Monvel, L.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 4 |a The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 /  |c Victor Guillemin, L. Boutet de Monvel. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2016] 
264 4 |c ©1981 
300 |a 1 online resource (166 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 0 |a Annals of Mathematics Studies ;  |v 99 
505 0 0 |t Frontmatter --   |t TABLE OF CONTENTS --   |t §1. Introduction --   |t §2. GENERALIZED TOEPLITZ OPERATORS --   |t §3. FOURIER INTEGRAL OPERATORS OF HERMITE TYPE --   |t §4. THE METAPLECTIC REPRESENTATION --   |t §5. METALINEAR AND METAPLECTIC STRUCTURES ON MANIFOLDS --   |t §6. ISOTROPIC SUBSPACES OF SYMPLECTIC VECTOR SPACES --   |t §7. THE COMPOSITION THEOREM --   |t §8. THE PROOF OF THEOREM 7.5 --   |t §9. PULL-BACKS, PUSH-FORWARDS AND EXTERIOR TENSOR PRODUCTS --   |t §10. THE TRANSPORT EQUATION --   |t §11. SYMBOLIC PROPERTIES OF TOEPLITZ OPERATORS --   |t §12. THE TRACE FORMULA --   |t §13. SPECTRAL PROPERTIES OF TOEPLITZ OPERATORS --   |t §14. THE HILBERT POLYNOMIAL --   |t §15. SOME CONCLUDING REMARKS --   |t BIBLIOGRAPHY --   |t APPENDIX: QUANTIZED CONTACT STRUCTURES --   |t Backmatter 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Spectral theory (Mathematics). 
650 0 |a Toeplitz operators. 
650 7 |a MATHEMATICS / Calculus.  |2 bisacsh 
653 |a Algebraic variety. 
653 |a Asymptotic analysis. 
653 |a Asymptotic expansion. 
653 |a Big O notation. 
653 |a Boundary value problem. 
653 |a Change of variables. 
653 |a Chern class. 
653 |a Codimension. 
653 |a Cohomology. 
653 |a Compact group. 
653 |a Complex manifold. 
653 |a Complex vector bundle. 
653 |a Connection form. 
653 |a Contact geometry. 
653 |a Corollary. 
653 |a Cotangent bundle. 
653 |a Curvature form. 
653 |a Diffeomorphism. 
653 |a Differentiable manifold. 
653 |a Dimensional analysis. 
653 |a Discrete spectrum. 
653 |a Eigenvalues and eigenvectors. 
653 |a Elaboration. 
653 |a Elliptic operator. 
653 |a Embedding. 
653 |a Equivalence class. 
653 |a Existential quantification. 
653 |a Exterior (topology). 
653 |a Fourier integral operator. 
653 |a Fourier transform. 
653 |a Hamiltonian vector field. 
653 |a Holomorphic function. 
653 |a Homogeneous function. 
653 |a Hypoelliptic operator. 
653 |a Integer. 
653 |a Integral curve. 
653 |a Integral transform. 
653 |a Invariant subspace. 
653 |a Lagrangian (field theory). 
653 |a Lagrangian. 
653 |a Limit point. 
653 |a Line bundle. 
653 |a Linear map. 
653 |a Mathematics. 
653 |a Metaplectic group. 
653 |a Natural number. 
653 |a Normal space. 
653 |a One-form. 
653 |a Open set. 
653 |a Operator (physics). 
653 |a Oscillatory integral. 
653 |a Parallel transport. 
653 |a Parameter. 
653 |a Parametrix. 
653 |a Periodic function. 
653 |a Polynomial. 
653 |a Projection (linear algebra). 
653 |a Projective variety. 
653 |a Pseudo-differential operator. 
653 |a Q.E.D. 
653 |a Quadratic form. 
653 |a Quantity. 
653 |a Quotient ring. 
653 |a Real number. 
653 |a Scientific notation. 
653 |a Self-adjoint. 
653 |a Smoothness. 
653 |a Spectral theorem. 
653 |a Spectral theory. 
653 |a Square root. 
653 |a Submanifold. 
653 |a Summation. 
653 |a Support (mathematics). 
653 |a Symplectic geometry. 
653 |a Symplectic group. 
653 |a Symplectic manifold. 
653 |a Symplectic vector space. 
653 |a Tangent space. 
653 |a Theorem. 
653 |a Todd class. 
653 |a Toeplitz algebra. 
653 |a Toeplitz matrix. 
653 |a Toeplitz operator. 
653 |a Trace formula. 
653 |a Transversal (geometry). 
653 |a Trigonometric functions. 
653 |a Variable (mathematics). 
653 |a Vector bundle. 
653 |a Vector field. 
653 |a Vector space. 
653 |a Volume form. 
653 |a Wave front set. 
700 1 |a Guillemin, Victor,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Annals of Mathematics eBook-Package 1940-2020  |z 9783110494914  |o ZDB-23-PMB 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Archive 1927-1999  |z 9783110442496 
776 0 |c print  |z 9780691082790 
856 4 0 |u https://doi.org/10.1515/9781400881444 
856 4 0 |u https://www.degruyter.com/isbn/9781400881444 
856 4 2 |3 Cover  |u https://www.degruyter.com/document/cover/isbn/9781400881444/original 
912 |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999  |c 1927  |d 1999 
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