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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Boutet de Monvel, L., author. aut http://id.loc.gov/vocabulary/relators/aut The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / Victor Guillemin, L. Boutet de Monvel. Princeton, NJ : Princeton University Press, [2016] ©1981 1 online resource (166 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 99 Frontmatter -- TABLE OF CONTENTS -- §1. Introduction -- §2. GENERALIZED TOEPLITZ OPERATORS -- §3. FOURIER INTEGRAL OPERATORS OF HERMITE TYPE -- §4. THE METAPLECTIC REPRESENTATION -- §5. METALINEAR AND METAPLECTIC STRUCTURES ON MANIFOLDS -- §6. ISOTROPIC SUBSPACES OF SYMPLECTIC VECTOR SPACES -- §7. THE COMPOSITION THEOREM -- §8. THE PROOF OF THEOREM 7.5 -- §9. PULL-BACKS, PUSH-FORWARDS AND EXTERIOR TENSOR PRODUCTS -- §10. THE TRANSPORT EQUATION -- §11. SYMBOLIC PROPERTIES OF TOEPLITZ OPERATORS -- §12. THE TRACE FORMULA -- §13. SPECTRAL PROPERTIES OF TOEPLITZ OPERATORS -- §14. THE HILBERT POLYNOMIAL -- §15. SOME CONCLUDING REMARKS -- BIBLIOGRAPHY -- APPENDIX: QUANTIZED CONTACT STRUCTURES -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Spectral theory (Mathematics). Toeplitz operators. MATHEMATICS / Calculus. bisacsh Algebraic variety. Asymptotic analysis. Asymptotic expansion. Big O notation. Boundary value problem. Change of variables. Chern class. Codimension. Cohomology. Compact group. Complex manifold. Complex vector bundle. Connection form. Contact geometry. Corollary. Cotangent bundle. Curvature form. Diffeomorphism. Differentiable manifold. Dimensional analysis. Discrete spectrum. Eigenvalues and eigenvectors. Elaboration. Elliptic operator. Embedding. Equivalence class. Existential quantification. Exterior (topology). Fourier integral operator. Fourier transform. Hamiltonian vector field. Holomorphic function. Homogeneous function. Hypoelliptic operator. Integer. Integral curve. Integral transform. Invariant subspace. Lagrangian (field theory). Lagrangian. Limit point. Line bundle. Linear map. Mathematics. Metaplectic group. Natural number. Normal space. One-form. Open set. Operator (physics). Oscillatory integral. Parallel transport. Parameter. Parametrix. Periodic function. Polynomial. Projection (linear algebra). Projective variety. Pseudo-differential operator. Q.E.D. Quadratic form. Quantity. Quotient ring. Real number. Scientific notation. Self-adjoint. Smoothness. Spectral theorem. Spectral theory. Square root. Submanifold. Summation. Support (mathematics). Symplectic geometry. Symplectic group. Symplectic manifold. Symplectic vector space. Tangent space. Theorem. Todd class. Toeplitz algebra. Toeplitz matrix. Toeplitz operator. Trace formula. Transversal (geometry). Trigonometric functions. Variable (mathematics). Vector bundle. Vector field. Vector space. Volume form. Wave front set. Guillemin, Victor, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691082790 https://doi.org/10.1515/9781400881444 https://www.degruyter.com/isbn/9781400881444 Cover https://www.degruyter.com/document/cover/isbn/9781400881444/original |
language |
English |
format |
eBook |
author |
Boutet de Monvel, L., Boutet de Monvel, L., Guillemin, Victor, |
spellingShingle |
Boutet de Monvel, L., Boutet de Monvel, L., Guillemin, Victor, The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / Annals of Mathematics Studies ; Frontmatter -- TABLE OF CONTENTS -- §1. Introduction -- §2. GENERALIZED TOEPLITZ OPERATORS -- §3. FOURIER INTEGRAL OPERATORS OF HERMITE TYPE -- §4. THE METAPLECTIC REPRESENTATION -- §5. METALINEAR AND METAPLECTIC STRUCTURES ON MANIFOLDS -- §6. ISOTROPIC SUBSPACES OF SYMPLECTIC VECTOR SPACES -- §7. THE COMPOSITION THEOREM -- §8. THE PROOF OF THEOREM 7.5 -- §9. PULL-BACKS, PUSH-FORWARDS AND EXTERIOR TENSOR PRODUCTS -- §10. THE TRANSPORT EQUATION -- §11. SYMBOLIC PROPERTIES OF TOEPLITZ OPERATORS -- §12. THE TRACE FORMULA -- §13. SPECTRAL PROPERTIES OF TOEPLITZ OPERATORS -- §14. THE HILBERT POLYNOMIAL -- §15. SOME CONCLUDING REMARKS -- BIBLIOGRAPHY -- APPENDIX: QUANTIZED CONTACT STRUCTURES -- Backmatter |
author_facet |
Boutet de Monvel, L., Boutet de Monvel, L., Guillemin, Victor, Guillemin, Victor, Guillemin, Victor, |
author_variant |
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author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Guillemin, Victor, Guillemin, Victor, |
author2_variant |
v g vg |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Boutet de Monvel, L., |
title |
The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / |
title_full |
The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / Victor Guillemin, L. Boutet de Monvel. |
title_fullStr |
The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / Victor Guillemin, L. Boutet de Monvel. |
title_full_unstemmed |
The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / Victor Guillemin, L. Boutet de Monvel. |
title_auth |
The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / |
title_alt |
Frontmatter -- TABLE OF CONTENTS -- §1. Introduction -- §2. GENERALIZED TOEPLITZ OPERATORS -- §3. FOURIER INTEGRAL OPERATORS OF HERMITE TYPE -- §4. THE METAPLECTIC REPRESENTATION -- §5. METALINEAR AND METAPLECTIC STRUCTURES ON MANIFOLDS -- §6. ISOTROPIC SUBSPACES OF SYMPLECTIC VECTOR SPACES -- §7. THE COMPOSITION THEOREM -- §8. THE PROOF OF THEOREM 7.5 -- §9. PULL-BACKS, PUSH-FORWARDS AND EXTERIOR TENSOR PRODUCTS -- §10. THE TRANSPORT EQUATION -- §11. SYMBOLIC PROPERTIES OF TOEPLITZ OPERATORS -- §12. THE TRACE FORMULA -- §13. SPECTRAL PROPERTIES OF TOEPLITZ OPERATORS -- §14. THE HILBERT POLYNOMIAL -- §15. SOME CONCLUDING REMARKS -- BIBLIOGRAPHY -- APPENDIX: QUANTIZED CONTACT STRUCTURES -- Backmatter |
title_new |
The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / |
title_sort |
the spectral theory of toeplitz operators. (am-99), volume 99 / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (166 p.) Issued also in print. |
contents |
Frontmatter -- TABLE OF CONTENTS -- §1. Introduction -- §2. GENERALIZED TOEPLITZ OPERATORS -- §3. FOURIER INTEGRAL OPERATORS OF HERMITE TYPE -- §4. THE METAPLECTIC REPRESENTATION -- §5. METALINEAR AND METAPLECTIC STRUCTURES ON MANIFOLDS -- §6. ISOTROPIC SUBSPACES OF SYMPLECTIC VECTOR SPACES -- §7. THE COMPOSITION THEOREM -- §8. THE PROOF OF THEOREM 7.5 -- §9. PULL-BACKS, PUSH-FORWARDS AND EXTERIOR TENSOR PRODUCTS -- §10. THE TRANSPORT EQUATION -- §11. SYMBOLIC PROPERTIES OF TOEPLITZ OPERATORS -- §12. THE TRACE FORMULA -- §13. SPECTRAL PROPERTIES OF TOEPLITZ OPERATORS -- §14. THE HILBERT POLYNOMIAL -- §15. SOME CONCLUDING REMARKS -- BIBLIOGRAPHY -- APPENDIX: QUANTIZED CONTACT STRUCTURES -- Backmatter |
isbn |
9781400881444 9783110494914 9783110442496 9780691082790 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA329 |
callnumber-sort |
QA 3329.2 B68 41981EB |
url |
https://doi.org/10.1515/9781400881444 https://www.degruyter.com/isbn/9781400881444 https://www.degruyter.com/document/cover/isbn/9781400881444/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.7/246 |
dewey-sort |
3515.7 3246 |
dewey-raw |
515.7/246 |
dewey-search |
515.7/246 |
doi_str_mv |
10.1515/9781400881444 |
oclc_num |
979970554 |
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The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / |
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tag="653" ind1=" " ind2=" "><subfield code="a">Spectral theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Spectral theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Square root.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Submanifold.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Summation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Support (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symplectic geometry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symplectic group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symplectic manifold.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symplectic vector space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tangent space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Todd class.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Toeplitz algebra.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Toeplitz matrix.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Toeplitz operator.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trace formula.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Transversal (geometry).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trigonometric functions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variable (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector bundle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector field.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Volume form.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Wave front set.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Guillemin, Victor, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton Annals of Mathematics eBook-Package 1940-2020</subfield><subfield code="z">9783110494914</subfield><subfield code="o">ZDB-23-PMB</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Archive 1927-1999</subfield><subfield code="z">9783110442496</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691082790</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400881444</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9781400881444</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9781400881444/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999</subfield><subfield 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