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1.

図書
図書
1. Experimental mathematics with Maple
Franco Vivaldi
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2001  xi, 223 p. ; 24 cm
シリーズ名: Chapman & Hall/CRC mathematics
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What is Maple? / 1：
Integers and rationals / 2：
Integers / 2.1：
Arithmetical expressions / 2.2：
Some Maple / 2.3：
Divisibility / 2.4：
Rationals / 2.5：
Primes / 2.6：
Standard library functions / 2.7：
Sets and functions / 3：
Sets / 3.1：
Sets with Maple / 3.2：
Functions / 3.3：
User-defined functions / 3.4：
Sequences / 4：
Basics / 4.1：
Sequences with Maple / 4.2：
Plotting the elements of a sequence / 4.3：
Periodic and eventually periodic sequences / 4.4：
Some non-periodic sequences / 4.5：
Basic counting sequences / 4.6：
Sequences defined recursively / 4.7：
Real and complex numbers / 5：
Digits of rationals / 5.1：
Real numbers / 5.2：
Random and pseudo-random digits* / 5.3：
Complex numbers / 5.4：
Structure of expressions / 5.5：
Analysis of an expression / 6.1：
More on substitutions / 6.2：
Functions acting on operands of expressions / 6.3：
Polynomials and rational functions / 7：
Polynomials / 7.1：
Polynomial arithmetic / 7.2：
Rational functions / 7.3：
Basic manipulations / 7.4：
Partial fractions decomposition* / 7.5：
Finite sums and products / 8：
Sums and products with Maple / 8.1：
Symbolic evaluation of sums and products / 8.3：
Double sums and products / 8.4：
Sums and products as recursive sequences / 8.5：
Elements of programming / 9：
Iteration / 9.1：
Study of an eventually periodic sequence / 9.2：
Conditional execution* / 9.3：
Procedures* / 9.4：
Vector spaces / 10：
Cartesian product of sets / 10.1：
Vectors with Maple / 10.2：
Matrices / 10.4：
Matrices with Maple / 10.5：
Modular arithmetic* / 11：
A modular system / 11.1：
Arithmetic of equivalence classes / 11.2：
Some arithmetical constructions in F[subscript p] / 11.3：
Some abstract structures* / 12：
The axioms of arithmetic / 12.1：
Metric spaces / 12.2：
Rings and fields / 12.3：
What is Maple? / 1：
Integers and rationals / 2：
Integers / 2.1：
2.

図書
図書
2. The curve shortening problem
Kai-Seng Chou, Xi-Ping Zhu
出版情報: Boca Raton, Flo. : Chapman & Hall/CRC, c2001  ix, 255 p. ; 24 cm
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Preface
Basic Results / 1：
Short time existence / 1.1：
Facts from the parabolic theory / 1.2：
The evolution of geometric quantities / 1.3：
Invariant Solutions for the Curve Shortening Flow / 2：
Travelling waves / 2.1：
Spirals / 2.2：
The support function of a convex curve / 2.3：
Self-similar solutions / 2.4：
The Curvature-Eikonal Flow for Convex Curves / 3：
Blaschke Selection Theorem / 3.1：
Preserving convexity and shrinking to a point / 3.2：
Gage-Hamilton Theorem / 3.3：
The contracting case of the ACEF / 3.4：
The stationary case of the ACEF / 3.5：
The expanding case of the ACEF / 3.6：
The Convex Generalized Curve Shortening Flow / 4：
Results from the Brunn-Minkowski Theory / 4.1：
The AGCSF for [sigma] in (1/3, 1) / 4.2：
The affine curve shortening flow / 4.3：
Uniqueness of self-similar solutions / 4.4：
The Non-convex Curve Shortening Flow / 5：
An isoperimetric ratio / 5.1：
Limits of the rescaled flow / 5.2：
Classification of singularities / 5.3：
A Class of Non-convex Anisotropic Flows / 6：
The decrease in total absolute curvature / 6.1：
The existence of a limit curve / 6.2：
Shrinking to a point / 6.3：
A whisker lemma / 6.4：
The convexity theorem / 6.5：
Embedded Closed Geodesics on Surfaces / 7：
Basic results / 7.1：
The limit curve / 7.2：
Convergence to a geodesic / 7.3：
The Non-convex Generalized Curve Shortening Flow / 8：
The number of convex arcs / 8.1：
Removal of interior singularities / 8.3：
The almost convexity theorem / 8.5：
Bibliography
Index
Preface
Basic Results / 1：
Short time existence / 1.1：
3.

図書
図書
3. An introduction to metric spaces and fixed point theory
Mohamed A. Khamsi, William A. Kirk
出版情報: New York : J. Wiley, c2001  x, 302 p. ; 25 cm
シリーズ名: A Wiley-Interscience publication
Pure and applied mathematics
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Preface
Metric Spaces
Introduction
Metric Contraction Principles
Hyperconvex Spaces
"Normal" Structures in Metric Spaces
Banach Spaces
Banach Spaces: Introduction
Continuous Mappings in Banach Spaces
Metric Fixed Point Theory
Banach Space Ultrapowers
Appendix: Set Theory
Bibliography
Index
Preface
Metric Spaces
Introduction
4.

図書
図書
4. Finite elements : theory, fast solvers, and applications in solid mechanics. 2nd ed (pbk.)
Dietrich Braess ; translated by Larry L. Schumaker
出版情報: Cambridge : Cambridge University Press, 2001  xvii, 352 p. ; 23 cm
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Preface to the Third English Edition page
Preface to the First English Edition
Preface to the German Edition
Notation
Introduction / Chapter I：
Examples and Classification of PDE's / 1：
Examples
Classification of PDE's
Well-posed Problems
Problems
The Maximum Principle / 2：
Corollaries
Problem
Finite Difference Methods / 3：
Discretization
Discrete maximum principle
A Convergence Theory for Difference Methods / 4：
Consistency
Local and global error
Limits of the convergence theory
Conforming Finite Elements / Chapter II：
Sobolev Spaces
Introduction to Sobolev spaces
Friedrichs' inequality
Possible singularities of H1 functions
Compact imbeddings
Variational Formulation of Elliptic Boundary-Value Problems of Second Order
Variational formulation
Reduction to homogeneous boundary conditions
Existence of solutions
Inhomogeneous boundary conditions
The Neumann Boundary-Value Problem. A Trace Theorem
Ellipticity in H1
Boundary-value problems with natural boundary conditions
Neumann boundary conditions
Mixed boundary conditions
Proof of the trace theorem
Practical consequences of the trace theorem
The Ritz-Galerkin Method and Some Finite Elements
Model Problem
Some Standard Finite Elements / 5：
Requirements on the meshes
Significance of the differentiability properties
Triangular elements with complete polynomials
Remarks on C1 elements
Bilinear elements
Quadratic rectangular elements
Affine families
Choice of an element
Approximation Properties / 6：
The Bramble-Hilbert lemma
Bilinear quadrilateral elements
Inverse estimates
Clément's interpolation
Appendix: On the optimality of the estimates
Error Bounds for Elliptic Problems of Second Order / 7：
Remarks on regularity
Error bounds in the energy norm
L2 estimates
A simple L? estimate
The L2-projector
Computational Considerations / 8：
Assembling the stiffness matrix
Static condensation
Complexity of setting up the matrix
Effect on the choice of a grid
Local mesh refinement
Implementation of the Neumann boundary-value Problem
Nonconforming and Other Methods / Chapter III：
Abstract Lemmas and a Simple Boundary Approximation
Generalizations of Céa's lemma
Duality methods
The Crouzeix-Raviart element
A Simple approximation to curved boundaries
Modifications of the duality argument
Isoparametric Elements
Isoparametric triangular elements
Isoparametric quadrilateral elements
Further Tools from Functional Analysis
Negative norms
Adjoint operators
An abstract existence theorem
An abstract convergence theorem
Proof of Theorem 3.4
Saddle Point Problems
Saddle points and minima
The inf-sup condition
Mixed finite element methods
Fortin interpolation
Saddle point problems with penalty term
Typical applications
Mixed Methods for the Poisson Equation
The Poisson equation as a mixed problem
The Raviart - Thomas element
Interpolation by Raviart-Thomas elements
Implementation and postprocessing
Mesh-dependent norms for the Raviart-Thomas element
The Softening behaviour of mixed methods
The Stokes Equation
Nearly incompressible flows
Finite Elements for the Stokes Problems
An instable element
The Taylor-Hood element
The MINI element
The divergence-free nonconforming P1 element
A Posteriori Error Estimates
Residual estimators
Lower estimates
Remark on other estimators
Local mesh refinement and convergence
A Posteriori Error Estimates via the Hypercircle Method / 9：
The Conjugate Gradient Method / Chapter IV：
Classical Iterative Methods for Solving Linear Systems
Stationary linear processes
The Jacobi and Gauss-Seidel methods
The model problem
Overrelaxation
Gradient Methods
The general gradient method
Gradient methods and quadratic functions
Convergence behavior in the case of large condition numbers
Conjugate Gradient and the Minimal Residual Method
The CG algorithm
Analysis of the CG method as an optimal method
The minimal residual method
Indefinite and unsymmetric matrices
Preconditioning
Preconditioning by SSOR
Preconditioning by ILU
Remarks on parallelization
Nonlinear Problems
The Uzawa algorithm and its variants
An alternative
Multigrid Methods / Chapter V：
Multigrid Methods for Variational Problems
Smoothing properties of classical iterative methods
The multigrid idea
The algorithm
Transfer between grids
Convergence of Multigrid Methods
Discrete norms
Connection with the Sobolev norm
Approximation property
Convergence proof for the two-grid method
An alternative short proof
Some variants
Convergence for Several Levels
A recurrence formula for the W-cycle
An improvement for the energy norm
The convergence proof for the V-cycle
Nested Iteration
Computation of starting values
Complexity
Multigrid methods with a small number of levels
The CASCADE algorithm
Multigrid Analysis via Space Decomposition
Schwarz alternating method
Assumptions
Direct consequences
Convergence of multiplicative methods
Verification of A1
Local mesh refinements
The multigrid-Newton method
The nonlinear multigrid method
Starting values
Finite Elements in Solid Mechanics / Chapter VI：
Introduction to Elasticity Theory
Kinematics
The equilibrium equations
The Piola transform
Constitutive Equations
Linear material laws
Hyperelastic Materials
Linear Elasticity Theory
The variational problem
The displacement formulation
The mixed method of Hellinger and Reissner
The mixed method of Hu and Washizu
Nearly incompressible material
Locking
Locking of the Timoshenko beam and typical remedies
Membranes
Plane stress states
Plane strain states
Membrane elements
The PEERS element
Beams and Plates: The Kirchhoff Plate
The hypotheses
Note on beam models
Mixed methods for the Kirchoff plate
DKT elements
The Mindlin-Reissner Plate
The Helmholtz decomposition
The mixed formulation with the Helmholtz decomposition
MITC elements
The Model without a Helmboltz decomposition
References
Index
Preface to the Third English Edition page
Preface to the First English Edition
Preface to the German Edition
5.

図書
図書
5. Quantum gauge theories : a true ghost story
Günter Scharf
出版情報: New York : J. Wiley, c2001  xi, 245 p. ; 25 cm
シリーズ名: A Wiley-Interscience publication
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Preface
Free fields / 1：
Bosonic scalar fields / 1.1：
Ferminoic scalar (ghost) fields / 1.2：
Massless vector fields / 1.3：
Operator gauge transformations / 1.4：
Massive vector fields / 1.5：
Fermionic vector (ghost) fields / 1.6：
Tensor fields / 1.7：
Spinor fields / 1.8：
Normally ordered products in free fields / 1.9：
Problems / 1.10：
Causal perturbation theory / 2：
The S-matrix in quantum mechanics / 2.1：
The method of Epstein and Glaser / 2.2：
Splitting of causal distributions in x-space / 2.3：
Splitting in momentum space / 2.4：
Calculation of tree graphs / 2.5：
Calculation of loop graphs / 2.6：
Normalizability / 2.7：
Spin-1 gauge theories: massless gauge fields / 2.8：
Perturbative gauge invariance / 3.1：
Self-coupling of gauge fields / 3.2：
Divergence and coboundary couplings / 3.3：
Yang-Mills theory to second order / 3.4：
Reductive Lie algebras / 3.5：
Coupling to matter fields / 3.6：
Gauge invariance to all orders / 3.7：
Unitarity / 3.8：
Other gauges / 3.9：
Gauge independence / 3.10：
Appendix A: Cauchy problem for the iterated wave equation / 3.11：
Spin-1 gauge theories: massive gauge fields / 3.12：
Massive QED and Abelian Higgs model / 4.1：
General massive gauge theory / 4.2：
First-order gauge invariance / 4.3：
Second-order gauge invariance / 4.4：
Third-order gauge invariance / 4.5：
Derivation of the electroweak gauge theory / 4.6：
Coupling to leptons / 4.7：
More fermionic families / 4.8：
Gauge invariance to third order: axial anomalies / 4.9：
Spin-2 gauge theory / 4.10：
Perturbative gauge invariance with tensor fields / 5.1：
The general spin-2 theory / 5.2：
Classification of spin-2 quantum gauge theories / 5.3：
Expansion of the Einstein-Hilbert Lagrangian / 5.5：
Q-vertex / 5.6：
Second-order gauge invariance: graviton sector / 5.7：
Second-order gauge invariance: ghost sector / 5.8：
Coupling to matter / 5.9：
Radiative corrections / 5.10：
Appendix B: Divergence couplings for gravity / 5.11：
Appendix C: General Q-vertex for quantum gravity / 5.12：
Bibliographical Notes / 5.13：
Index
Preface
Free fields / 1：
Bosonic scalar fields / 1.1：
6.

図書
図書
6. Strain solitons in solids and how to construct them
Alexander M. Samsonov
出版情報: Boca Raton : Chapman & Hall/CRC, c2001  xviii, 230 p. ; 25 cm
シリーズ名: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 117
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Nonlinear waves in elastic solids / 1：
Basic definitions / 1.1：
Wave terminology / 1.1.1：
Deformation and strains / 1.1.2：
Stresses / 1.1.3：
Physical and geometrical sources of nonlinearity / 1.2：
Elastic potentials and moduli / 1.2.1：
Compressibility, dispersion and dissipation in wave guides / 1.3：
A mathematical description of the general deformation wave problem / 2：
Action functional and the Lagrange formalism / 2.1：
Coupled equations of long wave propagation / 2.2：
One-dimensional quasi-hyperbolic equation / 2.3：
Derivation of the Doubly Dispersive Equation (DDE) / 2.3.1：
Refinement of the derivation of the DDE / 2.3.2：
Equations for wave in non-uniform highly nonlinear wave guide / 2.3.3：
Main assumptions and 2-D coupled equations / 2.4：
Waves in a wave guide embedded in an external medium / 2.5：
Direct methods and formal solutions / 3：
Nonlinear hyperbolic and evolution equations / 3.1：
Travelling wave solutions to the KdV and the DDE equations / 3.1.1：
Conservation laws / 3.2：
The Hamiltonian structure / 3.2.1：
Some notices in critical points analysis for an o.d.e. / 3.3：
New approach to a solution for an autonomous dissipative nonlinear equation / 3.4：
A general theorem of reduction / 3.5：
Dissipative equations with polynomial nonlinearity / 3.6：
Square and cubic polynomial nonlinearities / 3.6.1：
Physical interpretation of additional conditions for the travelling wave existence / 3.6.2：
Elliptic function solutions to higher order problems / 3.7：
Example of a nonlinear reaction-diffusion problem / 3.8：
Discontinuous solutions / 3.8.1：
Bounded periodical and solitary wave solutions / 3.8.2：
Autosoliton solution / 3.8.3：
Periodic bounded solutions in case [Delta] ] 0 / 3.8.4：
Nonlinear strain waves in elastic wave guides / 4：
Features of longitudinal waves in a rod / 4.1：
Experiments in nonlinear waves in solids / 4.2：
Strain soliton observation / 4.2.1：
Why is it a soliton? / 4.2.2：
Reflection of a strain soliton / 4.2.3：
Solitons in inhomogeneous rods / 4.3：
Solitons in the non-uniform rod / 4.3.1：
Solitons in the inhomogeneous rod / 4.3.2：
Experiments in soliton propagation in the non-uniform rod / 4.4：
Nonlinear waves in complex wave guides / 5：
Longitudinal nonlinear waves in an elastic plate / 5.1：
Generation and observation of the strain soliton in a plate / 5.1.1：
Longitudinal waves in rods embedded in a surrounding medium / 5.2：
Kinks in a rod in full contact with a surrounding medium / 5.2.1：
Waves in a rod in sliding contact with a surrounding medium / 5.2.2：
Statement and the solution to the problem / 5.2.3：
External stresses on the rod lateral surface / 5.2.4：
Derivation of strain-displacement relationships inside the rod / 5.2.5：
A nonlinear evolution equation for longitudinal strain waves along the rod and its solution / 5.2.6：
The influence of the external medium on the propagation of the strain soliton along the rod / 5.2.7：
A numerical simulation of unsteady strain wave propagation / 5.2.8：
Applications of the theory / 5.2.9：
Conclusions / 5.2.10：
Nonlinear waves in the layer upon the elastic half space / 5.3：
Physical background / 5.3.1：
Basic equations / 5.3.2：
The layer and the half-space contact with slippage / 5.3.3：
The full contact of the layer and the half-space / 5.3.4：
On various mathematical models of nonlinear waves in a layered medium / 5.3.5：
On physical experiments in waves in a layered medium / 5.3.6：
Numerical simulation of the solitary waves in solids / 6：
Numerical simulation of non-stationary deformation waves / 6.1：
Parametrisation of the strain solitary wave / 6.1.1：
Solitary waves in a homogeneous rod / 6.2：
Solitary waves in a nonuniform rod / 6.3：
Solitary waves in complex rods / 6.4：
Strain solitions in a rod with the periodically varied cross section / 6.4.1：
An example of classification using soliton transformation / 6.4.2：
Conclusive remarks and tentative applications
Bibliography
Appendix
Index
Nonlinear waves in elastic solids / 1：
Basic definitions / 1.1：
Wave terminology / 1.1.1：
7.

図書
図書
7. Geometric function theory and non-linear analysis
Tadeusz Iwaniec and Gaven Martin
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 2001  xv, 552 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
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8.

図書
図書
8. C[*]-algebras and numerical analysis
Roland Hagen, Steffen Roch, Bernd Silbermann
出版情報: New York : Marcel Dekker, c2001  376 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 236
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Preface
Introduction / 0：
Numerical analysis / 0.1：
Operator chemistry / 0.2：
The algebraic language of numerical analysis / 0.3：
Microscoping / 0.4：
A few remarks on economy / 0.5：
Brief description of the contents / 0.6：
Approximation methods / 1：
Basic definitions / 1.1.1：
Projection methods / 1.1.2：
Finite section method / 1.1.3：
Banach algebras and stability / 1.2：
Algebras, ideals and homomorphisms / 1.2.1：
Algebraization of stability / 1.2.2：
Small perturbations / 1.2.3：
Compact perturbations / 1.2.4：
Finite sections of Toeplitz operators with continuous generating function / 1.3：
Laurent, Toeplitz and Hankel operators / 1.3.1：
Invertibility and Fredholmness of Toeplitz operators / 1.3.2：
The finite section method / 1.3.3：
C*-algebras of approximation sequences / 1.4：
C*-algebras, their ideals and homomorphisms / 1.4.1：
The Toeplitz C*-algebra and the C*-algebra of the finite section method for Toeplitz operators / 1.4.2：
Stability of sequences in the C*-algebra of the finite section method for Toeplitz operators / 1.4.3：
Symbol of the finite section method for Toeplitz operators / 1.4.4：
Asymptotic behaviour of condition numbers / 1.5：
The condition of an operator / 1.5.1：
Convergence of norms / 1.5.2：
Condition numbers of finite sections of Toeplitz operators / 1.5.3：
Fractality of approximation methods / 1.6：
Fractal homomorphisms, fractal algebras, fractal sequences / 1.6.1：
Fractal algebras, and convergence of norms / 1.6.2：
Notes and references
Regularization of approximation methods / 2：
Stably regularizable sequences / 2.1：
Moore-Penrose inverses and regularizations of matrices / 2.1.1：
Moore-Penrose inverses and regularization of operators / 2.1.2：
Stably regularizable approximation sequences / 2.1.3：
Algebraic characterization of stably regularizable sequences / 2.2：
Moore-Penrose invertibility in C*-algebras / 2.2.1：
Stable regularizability, and Moore-Penrose invertibility in F/G / 2.2.2：
Finite sections of Toeplitz operators and their stable regularizability / 2.2.3：
Convergence of generalized condition numbers / 2.2.4：
Difficulties with Moore-Penrose stability / 2.2.5：
Approximation of spectra / 3：
Set sequences / 3.1：
Limiting sets of set functions / 3.1.1：
Coincidence of the partial and uniform limiting set / 3.1.2：
Spectra and their limiting sets / 3.2：
Limiting sets of spectra of norm convergent sequences / 3.2.1：
Limiting sets of spectra: the general case / 3.2.2：
The case of fractal sequences / 3.2.3：
Limiting sets of singular values / 3.2.4：
Pseudospectra and their limiting sets / 3.3：
[varepsilon]-invertibility / 3.3.1：
Limiting sets of pseudospectra / 3.3.2：
Pseudospectra of operator polynomials / 3.3.3：
Numerical ranges and their limiting sets / 3.4：
Spatial and algebraic numerical ranges / 3.4.1：
Limiting sets of numerical ranges / 3.4.2：
Stability analysis for concrete approximation methods / 3.4.3：
Local principles / 4.1：
Commutative C*-algebras / 4.1.1：
The local principle by Allan and Douglas / 4.1.2：
Fredholmness of Toeplitz operators with piecewise continuous generating function / 4.1.3：
Finite sections of Toeplitz operators generated by a piecewise continuous function / 4.2：
The lifting theorem / 4.2.1：
Application of the local principle / 4.2.2：
Galerkin methods with spline ansatz for singular integral equations / 4.2.3：
Finite sections of Toeplitz operators generated by a quasi-continuous function / 4.3：
Quasicontinuous functions / 4.3.1：
Stability of the finite section method / 4.3.2：
Some other classes of oscillating functions / 4.3.3：
Polynomial collocation methods for singular integral operators with piecewise continuous coefficients / 4.4：
Singular integral operators / 4.4.1：
Stability of the polynomial collocation method / 4.4.2：
Collocation versus Galerkin methods / 4.4.3：
Paired circulants and spline approximation methods / 4.5：
Circulants and paired circulants / 4.5.1：
The stability theorem / 4.5.2：
Finite sections of band-dominated operators / 4.6：
Multidimensional band dominated operators / 4.6.1：
Fredholmness of band dominated operators / 4.6.2：
Finite sections of band dominated operators / 4.6.3：
Representation theory / 5：
Representations / 5.1：
The spectrum of a C*-algebra / 5.1.1：
Primitive ideals / 5.1.2：
The spectrum of an ideal and of a quotient / 5.1.3：
Representations of some concrete algebras / 5.1.4：
Postliminal algebras / 5.2：
Liminal and postliminal algebras / 5.2.1：
Dual algebras / 5.2.2：
Finite sections of Wiener-Hopf operators with almost periodic generating function / 5.2.3：
Lifting theorems and representation theory / 5.3：
Lifting one ideal / 5.3.1：
Sufficient families of homomorphisms / 5.3.2：
Structure of fractal lifting homomorphisms / 5.3.4：
Fredholm sequences / 6：
Fredholm sequences in standard algebras / 6.1：
The standard model / 6.1.1：
Fredholm sequences and stable regularizability / 6.1.2：
Fredholm sequences and Moore-Penrose stability / 6.1.4：
Fredholm sequences and the asymptotic behavior of singular values / 6.2：
The main result / 6.2.1：
A distinguished element and its range dimension / 6.2.2：
Upper estimate of dim Im [Pi subscript n] / 6.2.3：
Lower estimate of dim Im [Pi subscript n] / 6.2.4：
Some examples / 6.2.5：
A general Fredholm theory / 6.3：
Centrally compact and Fredholm sequences / 6.3.1：
Fredholmness modulo compact elements / 6.3.2：
Weakly Fredholm sequences / 6.3.3：
Sequences with finite splitting property / 6.4.1：
Properties of weakly Fredholm sequences / 6.4.2：
Strong limits of weakly Fredholm sequences / 6.4.3：
Weakly Fredholm sequences of matrices / 6.4.4：
Some applications / 6.5：
Numerical determination of the kernel dimension / 6.5.1：
Around the finite section method for Toeplitz operators / 6.5.2：
Discretization of shift operators / 6.5.3：
Self-adjoint approximation sequences / 7：
The spectrum of a self-adjoint approximation sequence / 7.1：
Essential and transient points / 7.1.1：
Fractality of self-adjoint sequences / 7.1.2：
Arveson dichotomy: band operators / 7.1.3：
Arveson dichotomy: standard algebras / 7.1.4：
Szego-type theorems / 7.2：
Folner and Szego algebras / 7.2.1：
Szego's theorem revisited / 7.2.2：
A further generalization of Szego's theorem / 7.2.3：
Algebras with unique tracial state / 7.2.4：
Bibliography
Index
Preface
Introduction / 0：
Numerical analysis / 0.1：
9.

雑誌
雑誌
9. Discrete and continuous dynamical systems. Series B
出版情報: Springfield, Mo. : Shouchuan Hu, c2001-
巻次年月次: Vol. 1, no. 1 (Feb. 2001)-
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10.

雑誌
雑誌
10. Journal of the Australian Mathematical Society
Australian Mathematical Society
出版情報: Canberra : Australian Mathematical Society, 2001-
巻次年月次: Vol. 70, pt. 1 (Feb. 2001)-
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