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101 0 $aeng
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181   $ctxt
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183   $acr
200 14$aThe Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 /$fL. Boutet de Monvel, Victor Guillemin
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©1981
215   $a1 online resource (168 pages)
225 0 $aAnnals of Mathematics Studies ;$v240
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08279-0 
311   $a0-691-08284-7 
320   $aIncludes bibliographical references.
327   $tFrontmatter -- $tTABLE 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 -- $tBIBLIOGRAPHY -- $tAPPENDIX: QUANTIZED CONTACT STRUCTURES -- $tBackmatter
330   $aThe theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations.If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol.It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.
410  0$aAnnals of mathematics studies ;$vNumber 99.
606   $aToeplitz operators
606   $aSpectral theory (Mathematics)
610   $aAlgebraic variety.
610   $aAsymptotic analysis.
610   $aAsymptotic expansion.
610   $aBig O notation.
610   $aBoundary value problem.
610   $aChange of variables.
610   $aChern class.
610   $aCodimension.
610   $aCohomology.
610   $aCompact group.
610   $aComplex manifold.
610   $aComplex vector bundle.
610   $aConnection form.
610   $aContact geometry.
610   $aCorollary.
610   $aCotangent bundle.
610   $aCurvature form.
610   $aDiffeomorphism.
610   $aDifferentiable manifold.
610   $aDimensional analysis.
610   $aDiscrete spectrum.
610   $aEigenvalues and eigenvectors.
610   $aElaboration.
610   $aElliptic operator.
610   $aEmbedding.
610   $aEquivalence class.
610   $aExistential quantification.
610   $aExterior (topology).
610   $aFourier integral operator.
610   $aFourier transform.
610   $aHamiltonian vector field.
610   $aHolomorphic function.
610   $aHomogeneous function.
610   $aHypoelliptic operator.
610   $aInteger.
610   $aIntegral curve.
610   $aIntegral transform.
610   $aInvariant subspace.
610   $aLagrangian (field theory).
610   $aLagrangian.
610   $aLimit point.
610   $aLine bundle.
610   $aLinear map.
610   $aMathematics.
610   $aMetaplectic group.
610   $aNatural number.
610   $aNormal space.
610   $aOne-form.
610   $aOpen set.
610   $aOperator (physics).
610   $aOscillatory integral.
610   $aParallel transport.
610   $aParameter.
610   $aParametrix.
610   $aPeriodic function.
610   $aPolynomial.
610   $aProjection (linear algebra).
610   $aProjective variety.
610   $aPseudo-differential operator.
610   $aQ.E.D.
610   $aQuadratic form.
610   $aQuantity.
610   $aQuotient ring.
610   $aReal number.
610   $aScientific notation.
610   $aSelf-adjoint.
610   $aSmoothness.
610   $aSpectral theorem.
610   $aSpectral theory.
610   $aSquare root.
610   $aSubmanifold.
610   $aSummation.
610   $aSupport (mathematics).
610   $aSymplectic geometry.
610   $aSymplectic group.
610   $aSymplectic manifold.
610   $aSymplectic vector space.
610   $aTangent space.
610   $aTheorem.
610   $aTodd class.
610   $aToeplitz algebra.
610   $aToeplitz matrix.
610   $aToeplitz operator.
610   $aTrace formula.
610   $aTransversal (geometry).
610   $aTrigonometric functions.
610   $aVariable (mathematics).
610   $aVector bundle.
610   $aVector field.
610   $aVector space.
610   $aVolume form.
610   $aWave front set.
615  0$aToeplitz operators.
615  0$aSpectral theory (Mathematics)
676   $a515.7/246
700   $aBoutet de Monvel$b L., $060656
702   $aGuillemin$b Victor, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154743403321
996   $aThe Spectral Theory of Toeplitz Operators. (AM-99), Volume 99$92788875
997   $aUNINA