Spectral Theory of Toeplitz Operators
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A01=L. Boutet de Monvel
A01=Louis Boutet De Monvel
A01=Victor Guillemin
Algebraic variety
Asymptotic analysis
Asymptotic expansion
Author_L. Boutet de Monvel
Author_Louis Boutet De Monvel
Author_Victor Guillemin
Big O notation
Boundary value problem
Category=PBKF
Change of variables
Codimension
Cohomology
Complex manifold
Complex vector bundle
Connection form
Contact geometry
Cotangent bundle
Curvature form
Diffeomorphism
Differentiable manifold
Dimensional analysis
Eigenvalues and eigenvectors
Elliptic operator
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
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)
Limit point
Line bundle
Linear map
Metaplectic group
Natural number
One-form
Open set
Operator (physics)
Parametrix
Periodic function
Polynomial
Projection (linear algebra)
Projective variety
Pseudo-differential operator
Quadratic form
Quotient ring
Scientific notation
Self-adjoint
Spectral theorem
Spectral theory
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
Trigonometric functions
Vector bundle
Vector space
Volume form
Product details
- ISBN 9780691082790
- Weight: 255g
- Dimensions: 152 x 229mm
- Publication Date: 21 Aug 1981
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
