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Infinitesimal dimensional topology.
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ISBN: 0691080879 1400881404 9780691080871 Year: 1972 Volume: 69 Publisher: Princeton (N.J.) : Princeton university press,

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Abstract

In essence the proceedings of the 1967 meeting in Baton Rouge, the volume offers significant papers in the topology of infinite dimensional linear spaces, fixed point theory in infinite dimensional spaces, infinite dimensional differential topology, and infinite dimensional pointset topology. Later results of the contributors underscore the basic soundness of this selection, which includes survey and expository papers, as well as reports of continuing research.

Keywords

Topology --- Differential geometry. Global analysis --- Differential topology --- Functional analysis --- Congresses --- Analyse fonctionnnelle --- Geometry, Differential --- Anderson's theorem. --- Annihilator (ring theory). --- Automorphism. --- Baire measure. --- Banach algebra. --- Banach manifold. --- Banach space. --- Bounded operator. --- Cartesian product. --- Characterization (mathematics). --- Cohomology. --- Compact space. --- Complement (set theory). --- Complete metric space. --- Connected space. --- Continuous function. --- Convex set. --- Coset. --- Critical point (mathematics). --- Diagram (category theory). --- Differentiable manifold. --- Differential topology. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dual space. --- Duality (mathematics). --- Endomorphism. --- Equivalence class. --- Euclidean space. --- Existential quantification. --- Explicit formulae (L-function). --- Exponential map (Riemannian geometry). --- Fixed-point theorem. --- Fréchet derivative. --- Fréchet space. --- Fuchsian group. --- Function space. --- Fundamental class. --- Haar measure. --- Hessian matrix. --- Hilbert space. --- Homeomorphism. --- Homology (mathematics). --- Homotopy group. --- Homotopy. --- Inclusion map. --- Infimum and supremum. --- Lebesgue space. --- Lefschetz fixed-point theorem. --- Limit point. --- Linear space (geometry). --- Locally convex topological vector space. --- Loop space. --- Mathematical optimization. --- Measure (mathematics). --- Metric space. --- Module (mathematics). --- Natural topology. --- Neighbourhood (mathematics). --- Normal space. --- Normed vector space. --- Open set. --- Ordinal number. --- Paracompact space. --- Partition of unity. --- Path space. --- Product topology. --- Quantifier (logic). --- Quotient space (linear algebra). --- Quotient space (topology). --- Radon measure. --- Reflexive space. --- Representation theorem. --- Riemannian manifold. --- Schauder fixed point theorem. --- Sign (mathematics). --- Simply connected space. --- Space form. --- Special case. --- Stiefel manifold. --- Strong operator topology. --- Subcategory. --- Submanifold. --- Subset. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological space. --- Topological vector space. --- Topology. --- Transfinite induction. --- Transfinite. --- Transversal (geometry). --- Transversality theorem. --- Tychonoff cube. --- Union (set theory). --- Unit sphere. --- Weak topology. --- Weakly compact. --- Differential topology - Congresses --- Functional analysis - Congresses --- Topology - Congresses --- Analyse fonctionnelle.

The spectral theory of Toeplitz operators
Authors: ---
ISBN: 0691082847 0691082790 1400881447 9780691082844 Year: 1981 Volume: 99 Publisher: Princeton (N.J.): Princeton university press,

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Abstract

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.

Keywords

Operator theory --- Toeplitz operators --- Spectral theory (Mathematics) --- 517.984 --- Spectral theory of linear operators --- Toeplitz operators. --- Spectral theory (Mathematics). --- 517.984 Spectral theory of linear operators --- Operators, Toeplitz --- Linear operators --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- 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. --- Opérateurs pseudo-différentiels

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