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1.

電子ブック
ＥＢ
1. Construction of Global Lyapunov Functions Using Radial Basis Functions
Peter Giesl, J.M Morel, F. Takens
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2007
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Introduction / 1：
An Example: Chemostat / 1.1：
Lyapunov Functions and Radial Basis Functions / 1.2：
Overview / 1.3：
Lyapunov Functions / 2：
Introduction to Dynamical Systems / 2.1：
Basic Definitions and Concepts / 2.1.1：
Local Lyapunov Functions / 2.1.2：
The Function [characters not reproducible] (Jordan Normal Form) / 2.2.1：
The Function [characters not reproducible] (Matrix Equation) / 2.2.2：
Summary and Example / 2.2.3：
Global Lyapunov Functions / 2.3：
The Lyapunov Function T with Constant Orbital Derivative / 2.3.1：
Level Sets of Lyapunov Functions / 2.3.2：
The Lyapunov Function V Defined in A(x[subscript 0]) / 2.3.3：
Taylor Polynomial of V / 2.3.4：
Summary and Examples / 2.3.5：
Radial Basis Functions / 3：
Approximation / 3.1：
Approximation via Function Values / 3.1.1：
Approximation via Orbital Derivatives / 3.1.2：
Mixed Approximation / 3.1.3：
Wendland Functions / 3.1.4：
Native Space / 3.2：
Characterization of the Native Space / 3.2.1：
Positive Definiteness of the Interpolation Matrices / 3.2.2：
Error Estimates / 3.2.3：
Construction of Lyapunov Functions / 4：
Non-Local Part / 4.1：
Local Part / 4.2：
Local Lyapunov Basin / 4.2.1：
Local Lyapunov Function / 4.2.2：
Taylor Polynomial / 4.2.3：
Global Determination of the Basin of Attraction / 5：
Approximation via a Single Operator / 5.1：
Approximation via Orbital Derivatives and Function Values / 5.1.1：
Stepwise Exhaustion of the Basin of Attraction / 5.2.2：
Application of the Method: Examples / 6：
Combination of a Local and Non-Local Lyapunov Function / 6.1：
Description / 6.1.1：
Examples / 6.1.2：
Approximation via Taylor Polynomial / 6.2：
Stepwise Exhaustion Using Mixed Approximation / 6.2.1：
Example / 6.3.1：
Conclusion / 6.4：
Appendices
Distributions and Fourier Transformation / A：
Distributions / A.1：
Fourier Transformation / A.2：
Data / B：
Figures / B.1：
Notations / C：
References
Index
Introduction / 1：
An Example: Chemostat / 1.1：
Lyapunov Functions and Radial Basis Functions / 1.2：
2.

電子ブック
ＥＢ
2. Continuous Strong Markov Processes in Dimension One
Sigurd Assing, Wolfgang Schmidt, A. Dold, Wolfgang M. Schmidt, F. Takens, Bernard Teissier
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 1998
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3.

電子ブック
ＥＢ
3. Cubic Metaplectic Forms and Theta Functions
Nikolai Proskurin, A. Dold, F. Takens
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 1998
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4.

電子ブック
ＥＢ
4. Differentiability of Six Operators on Nonsmooth Functions and p-Variation
Richard M. Dudley, R. Norvaisa, Rimas Norvaisa, J. Qian, F. Takens, Bernard Teissier
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 1999
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Preface
A survey on differentiability of six operators in relation to probability and statistics / Part I：
Contents of Part I
Introduction; kinds of differentiability / 1：
The two-function composition operator (F,G) &prompto; F&rbull;G / 2：
The quantile (inverse) operator / 3：
The integration operator and Young integrals / 4：
The product integral / 5：
Probability and p-vaxiation / 6：
General and C-differentiability / 7：
The chain rule and concluding remarks / 8：
Appendices
References
Product integrals, Young integrals and p-variation / Part II：
Abstract
Contents of Part II
Introduction
p-variation
Stieltjes and Young integrals
Product integrals
Indefinite product integrals
The logarithm operator
Differentiability of the composition and inverse operators for regulated and a.e. continuous functions / Part III：
Contents of Part III
Regulated functions
Almost everywhere continuous functions
The quantile operator
The composition operator for real-valued functions
The composition operator for Banach-valued functions
Appendix
Bibliographies on p-variation and φ-variation / R. M. Dudley ; R. Norvai&sbreve;a ; Jinghua QianPart IV：
Contents of Part IV
Bibliography on p-variation
Bibliography on φ-variation
Subject Index
Author Index
Preface
A survey on differentiability of six operators in relation to probability and statistics / Part I：
Contents of Part I
5.

電子ブック
ＥＢ
5. Flows on 2-dimensional Manifolds
Igor Nikolaev, A. Dold, F. Takens, Bernard Teissier, Evgeny Zhuzhoma
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 1999
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Definitions and examples / 1：
Preliminaries / 1.1：
Basic constructions / 1.2：
The projection method / 1.2.1：
The universal covering method / 1.2.2：
The suspension method / 1.2.3：
Whitney theorem / 1.2.4：
Connected sum of flows / 1.2.5：
The branch covering method / 1.2.6：
Basic examples / 1.3：
Gradient and Morse-Smale flows / 1.3.1：
Transitive flows / 1.3.2：
Flows with Cantor type limit sets / 1.3.3：
Area preserving and Hamiltonian flows / 1.3.4：
Harmonic and geodesic vector fields / 1.3.5：
Poincare-Bendixson's theory / 2：
Existence of closed transversal / 2.1：
Absence of non-trivial recurrent trajectories on some surfaces / 2.2：
Hilmy's and Cherry's theorems on quasiminimal sets / 2.3：
Maier's theorems on quasiminimal sets / 2.4：
Gutierrez's structure theorem / 2.5：
Limit set of individual trajectory / 2.6：
List of limit and minimal sets / 2.6.1：
Results of Solntzev and Vinograd / 2.6.2：
On the existence of minimal sets / 2.6.3：
Decomposition of flows / 3：
Decomposition theorems / 3.1：
Irreducible flows on torus / 3.1.1：
Canonical neighborhood / 3.1.2：
Gardiner - Levitt's decomposition / 3.1.3：
Pants decomposition / 3.1.4：
Decomposition of area preserving and Hamiltonian flows / 3.1.5：
Center of flow / 3.2：
Blowing-down of flows / 3.3：
Regular flows / 3.4：
Singular trajectories / 3.4.1：
Cells / 3.4.2：
Application: smoothing of flows / 3.5：
Local theory / 4：
Topological normal forms / 4.1：
Analytical normal forms / 4.2：
Smooth normal forms / 4.3：
Finitely smooth normal forms / 4.4：
Degenerate critical points / 4.5：
C1 normal forms of degenerate singularities / 4.6：
Space of flows and vector fields / 5：
Structural stability / 5.1：
Peixoto's graphs. Classification of Morse-Smale flows / 5.2：
Rotation systems / 5.2.1：
Peixoto theorems / 5.2.2：
Peixoto's counterexample revisited / 5.2.3：
Lyapunov's method / 5.3：
Lyapunov functions / 5.3.1：
Lyapunov graphs / 5.3.2：
Connected components of Morse-Smale flows / 5.4：
Degrees of non-stability / 5.5：
Typical properties of non-stable flows / 5.6：
Ergodic theory / 6：
Liouville's theorem / 6.1：
Kolmogorov's theorem for flows on torus / 6.2：
Non-trivial invariant measures / 6.3：
Ergodicity / 6.4：
Mixing / 6.5：
Entropy / 6.6：
Invariants of surface flows / 7：
Topological classification of torus flows / 7.1：
Rotation numbers / 7.1.1：
Classification of minimal flows / 7.1.2：
Classification of the Denjoy flows / 7.1.3：
Classification of flows of the Cherry type / 7.1.4：
Oriented surfaces of genus ≥ 2 / 7.2：
Aranson-Grines homotopy rotation class / 7.2.1：
Homotopy rotation orbit / 7.2.2：
Equivalence of irrational flows / 7.2.3：
Properties of the homotopy rotation classes / 7.2.4：
Application of geodesic laminations / 7.3：
Transitive flows on non-orientable surfaces / 7.4：
Torus with a cross-cup / 7.4.1：
Non-orientable surfaces of genus ≥ 4 / 7.4.2：
Classification of exceptional minimal sets / 7.5：
Classification of the regular flows / 7.6：
Leontovich-Maier's theorem for sphere flows / 7.6.1：
Neumann-O'Brien's orbit complex / 7.6.2：
Bolsinov-Fomenko's classification of Hamiltonian flows / 7.6.3：
Classification of non-wandering flows / 7.7：
Elementary cells of non-wandering flows / 7.7.1：
Conley-Lyapunov-Peixoto graphs / 7.7.2：
Equivalence Problem / 7.7.3：
Realization Problem / 7.7.4：
Cayley graph of a flow / 7.8：
Finite groups and Cayley graphs / 7.8.1：
Isomorphism Problem / 7.8.2：
Homology and cohomology invariants / 7.8.3：
Asymptotic cycles / 7.9.1：
Fundamental class of A. Katok / 7.9.2：
Zorich's cycles / 7.9.3：
Rotation sets of surface flows / 7.10：
Smooth classification of flows / 7.11：
Torus and Klein bottle / 7.11.1：
Closed orientable surfaces of genus ≥ 2 / 7.11.2：
C*-algebras of surface flows / 8：
Irrational rotation algebra / 8.1：
Dimension groups / 8.1.1：
Continued fractions / 8.1.2：
Effros-Shen's Theorem / 8.1.3：
Embedding of Aα / 8.1.4：
Projections of Aα / 8.1.5：
Morita Equivalence / 8.1.6：
Artin's rotation algebra / 8.2：
Myrberg's Approximationssatz / 8.2.1：
Artin's numbers / 8.2.2：
K-theory / 8.3：
Torus with Reeb's components / 8.3.1：
Baum-Connes Conjecture / 8.3.2：
C*-algebras of Morse-Smale flows / 8.4：
Semi-local theory / 9：
Denjoy's and Schwarz's theorems / 9.1：
Cherry's problem / 9.2：
Local structure preventing quasiminimality / 9.3：
Anosov-Weil problem / 10：
Theorems of Weil and Anosov / 10.1：
Asymptotic directions / 10.1.1：
Weil's theorem and Weil's conjecture / 10.1.2：
Anosov's theorem / 10.1.3：
Proof of Weil's conjecture and Weil's theorem / 10.1.4：
Asymptotic direction of individual curves / 10.2：
Non-trivial recurrent semi-trajectories / 10.2.1：
Trajectories of analytic flows / 10.2.2：
Leaves of foliation / 10.2.3：
Curves with restriction on the geodesic curvature / 10.2.4：
Approximation of curve by trajectories of a flow / 10.3：
Limit sets of curves and trajectories at the absolute / 10.4：
Deviation of curves from the geodesies / 10.5：
The deviation property of trajectories / 10.5.1：
Deviation from the geodesic frameworks / 10.5.2：
Branched coverings / 10.5.3：
Swing of trajectories near hyperbolic lines / 10.5.4：
Examples of unbounded deviation / 10.6：
Surfaces of genus ≥ 2 / 10.6.1：
Irrational direction on torus / 10.6.2：
Rational direction on torus / 10.6.3：
Non-compact surfaces / 11：
Kaplan's classification / 11.1：
Level curves of harmonic functions / 11.2：
Markus's classification / 11.3：
Neumann's example / 11.4：
Inaba's example and Beniere-Meigniez's theorem / 11.6：
Beniere-Hector's theorem / 11.7：
Aranson-Zhuzhoma's example / 11.8：
Triptych / 12：
Geodesic frameworks revisited / 12.1：
On continuity and collapse of geodesic frameworks / 12.2：
Cr-closing lemma / 12.3：
Definitions and examples / 1：
Preliminaries / 1.1：
Basic constructions / 1.2：
6.

電子ブック
ＥＢ
6. Fluctuation Theory for Lévy Processes
Ronald A. Doney, J.-M Morel, Jean Picard, F. Takens
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2007
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Introduction to Levy Processes / 1：
Notation / 1.1：
Poisson Point Processes / 1.2：
The Levy-Ito Decomposition / 1.3：
Levy Processes as Markov Processes / 1.4：
Subordinators / 2：
Introduction / 2.1：
Basics / 2.2：
The Renewal Measure / 2.3：
Passage Across a Level / 2.4：
Arc-Sine Laws for Subordinators / 2.5：
Rates of Growth / 2.6：
Killed Subordinators / 2.7：
Local Times and Excursions / 3：
Local Time of a Markov Process / 3.1：
The Regular, Instantaneous Case / 3.3：
The Excursion Process / 3.4：
The Case of Holding and Irregular Points / 3.5：
Ladder Processes and the Wiener-Hopf Factorisation / 4：
The Random Walk Case / 4.1：
The Reflected and Ladder Processes / 4.3：
Applications / 4.4：
A Stochastic Bound / 4.5：
Further Wiener-Hopf Developments / 5：
Extensions of a Result due to Baxter / 5.1：
Les Equations Amicales of Vigon / 5.3：
A First Passage Quintuple Identity / 5.4：
Creeping and Related Questions / 6：
Notation and Preliminary Results / 6.1：
The Mean Ladder Height Problem / 6.3：
Creeping / 6.4：
Limit Points of the Supremum Process / 6.5：
Regularity of the Half-Line / 6.6：
Summary: Four Integral Tests / 6.7：
Spitzer's Condition / 7：
Proofs / 7.1：
The Case [rho] = 0, 1 / 7.2.1：
A First Proof for the Case 0 < [rho] < 1 / 7.2.2：
A Second Proof for the Case 0 < [rho] < 1 / 7.2.3：
Further Results / 7.3：
Tailpiece / 7.4：
Levy Processes Conditioned to Stay Positive / 8：
Notation and Preliminaries / 8.1：
Definition and Path Decomposition / 8.3：
The Convergence Result / 8.4：
Pathwise Constructions of (X, P[superscript uparrow]) / 8.5：
Tanaka's Construction / 8.5.1：
Bertoin's Construction / 8.5.2：
Spectrally Negative Levy Processes / 9：
The Scale Function / 9.1：
Further Developments / 9.5：
Exit Problems for the Reflected Process / 9.6：
Addendum / 9.7：
Small-Time Behaviour / 10：
Convergence in Probability / 10.1：
Almost Sure Results / 10.4：
Summary of Asymptotic Results / 10.5：
Laws of Large Numbers / 10.5.1：
Central Limit Theorems / 10.5.2：
Exit from a Symmetric Interval / 10.5.3：
References
Index
List of Participants
List of Short Lectures
Introduction to Levy Processes / 1：
Notation / 1.1：
Poisson Point Processes / 1.2：
7.

電子ブック
ＥＢ
7. Forward-Backward Stochastic Differential Equations and their Applications
Jin Ma, J.-M Morel, F. Takens, Jiongmin Yong
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2007
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Preface
Introduction
Linear Equations
Method of Optimal Control
Four Step Scheme
Linear, Degenerate Backward Stochastic Partial Differential Equations
The Method of Continuation
FBSDEs with Reflections
Applications of FBSDEs
Numerical Methods for FBSDEs
Comments and Remarks
References
Index
Preface
Introduction
Linear Equations
8.

電子ブック
ＥＢ
8. Foundations of Grothendieck Duality for Diagrams of Schemes
Joseph Lipman, Mitsuyasu Hashimoto, F. Takens, F. Takens, B. Teissier. edited by J.-M. Morel, B. Teissier
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2009
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Joseph Lipman: Notes on Derived Functors and Grothendieck Duality / Part I：
Abstract
Introduction
Derived and Triangulated Categories / 1：
The Homotopy Category K / 1.1：
The Derived Category D / 1.2：
Mapping Cones / 1.3：
Triangulated Categories (?-Categories) / 1.4：
Triangle-Preserving Functors (?-Functors) / 1.5：
D-Subcategories / 1.6：
Localizing Subcategories of K; ?-Equivalent Categories / 1.7：
Examples / 1.8：
Complexes with Homology in a Plump Subcategory / 1.9：
Truncation Functors / 1.10：
Bounded Functors; Way-Out Lemma / 1.11：
Derived Functors / 2：
Definition of Derived Functors / 2.1：
Existence of Derived Functors / 2.2：
Right-Derived Functors via Injective Resolutions / 2.3：
Derived Homomorphism Functors / 2.4：
Derived Tensor Product / 2.5：
Adjoint Associativity / 2.6：
Acyclic Objects; Finite-Dimensional Derived Functors / 2.7：
Derived Direct and Inverse Image / 3：
Preliminaries / 3.1：
Adjointness of Derived Direct and Inverse Image / 3.2：
?-Adjoint Functors / 3.3：
Adjoint Functors between Monoidal Categories / 3.4：
Adjoint Functors between Closed Categories / 3.5：
Adjoint Monoidal ?-Pseudofunctors / 3.6：
More Formal Consequences: Projection, Base Change / 3.7：
Direct Sums / 3.8：
Concentrated Scheme-Maps / 3.9：
Independent Squares; Kunneth Isomorphism / 3.10：
Abstract Grothendieck Duality for Schemes / 4：
Global Duality / 4.1：
Sheafified Duality-Preliminary Form / 4.2：
Pseudo-Coherence and Quasi-Properness / 4.3：
Sheafified Duality, Base Change / 4.4：
Proof of Duality and Base Change: Outline / 4.5：
Steps in the Proof / 4.6：
Quasi-Perfect Maps / 4.7：
Two Fundamental Theorems / 4.8：
Perfect Maps of Noetherian Schemes / 4.9：
Appendix: Dualizing Complexes / 4.10：
References
Index
Mitsuyasu Hashimoto: Equivariant Twisted Inverses / Part II：
Commutativity of Diagrams Constructed from a Monoidal Pair of Pseudofunctors
Sheaves on Ringed Sites
Derived Categories and Derived Functors of Sheaves on Ringed Sites
Sheaves over a Diagram of S-Schemes
The Left and Right Inductions and the Direct and Inverse Images / 5：
Operations on Sheaves Via the Structure Data / 6：
Quasi-Coherent Sheaves Over a Diagram of Schemes / 7：
Derived Functors of Functors on Sheaves of Modules Over Diagrams of Schemes / 8：
Simplicial Objects / 9：
Descent Theory / 10：
Local Noetherian Property / 11：
Groupoid of Schemes / 12：
Bokstedt-Neeman Resolutions and HyperExt Sheaves / 13：
The Right Adjoint of the Derived Direct Image Functor / 14：
Comparison of Local Ext Sheaves / 15：
The Composition of Two Almost-Pseudofunctors / 16：
The Right Adjoint of the Derived Direct Image Functor of a Morphism of Diagrams / 17：
Commutativity of Twisted Inverse with Restrictions / 18：
Open Immersion Base Change / 19：
The Existence of Compactification and Composition Data for Diagrams of Schemes Over an Ordered Finite Category / 20：
Flat Base Change / 21：
Preservation of Quasi-Coherent Cohomology / 22：
Compatibility with Derived Direct Images / 23：
Compatibility with Derived Right Inductions / 24：
Equivariant Grothendieck's Duality / 25：
Morphisms of Finite Flat Dimension / 26：
Cartesian Finite Morphisms / 27：
Cartesian Regular Embeddings and Cartesian Smooth Morphisms / 28：
Group Schemes Flat of Finite Type / 29：
Compatibility with Derived G-Invariance / 30：
Equivariant Dualizing Complexes and Canonical Modules / 31：
A Generalization of Watanabe's Theorem / 32：
Other Examples of Diagrams of Schemes / 33：
Glossary
Joseph Lipman: Notes on Derived Functors and Grothendieck Duality / Part I：
Abstract
Introduction
9.

電子ブック
ＥＢ
9. From Hahn-Banach to Monotonicity
Stephen Simons, F. Takens
出版情報: SpringerLink Books - AutoHoldings , Springer Netherlands, 2008
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Introduction
The Hahn-Banach-Lagrange theorem and some consequences / I：
The Hahn-Banach-Lagrange theorem / 1：
Applications to functional analysis / 2：
A minimax theorem / 3：
The dual and bidual of a normed space / 4：
Excess, duality gap, and minimax criteria for weak compactness / 5：
Sharp Lagrange multiplier and KKT results / 6：
Fenchel duality / II：
A sharp version of the Fenchel Duality theorem / 7：
Fenchel duality with respect to a bilinear form - locally convex spaces / 8：
Some properties of 1/2||.||2 / 9：
The conjugate of a sum in the locally convex case / 10：
Fenchel duality vs the conjugate of a sum / 11：
The restricted biconjugate and Fenchel-Moreau points / 12：
Surrounding sets and the dom lemma / 13：
The ⊖-theorem / 14：
The Attouch-Brezis theorem / 15：
A bivariate Attouch-Brezis theorem / 16：
Multifunctions, SSD spaces, monotonicity and Fitzpatrick functions / III：
Multifunctions, monotonicity and maximality / 17：
Subdifferentials are maximally monotone / 18：
SSD spaces, q-positive sets and BC-functions / 19：
Maximally q-positive sets in SSD spaces / 20：
SSDB spaces / 21：
The SSD space E × E* / 22：
Fitzpatrick functions and fitzpatrifications / 23：
The maximal monotonicity of a sum / 24：
Monotone multifunctions on general Banach spaces / IV：
Monotone multifunctions with bounded range / 25：
A general local boundedness theorem / 26：
The six set theorem and the nine set theorem / 27：
D(Sφ) and various hulls / 28：
Monotone multifunctions on reflexive Banach spaces / V：
Criteria for maximality, and Rockafellar's surjectivity theorem / 29：
Surjectivity and an abstract Hammerstein theorem / 30：
The Brezis-Haraux condition / 31：
Bootstrapping the sum theorem / 32：
The > six set and the > nine set theorems for pairs of multifunctions / 33：
The Brezis-Crandall-Pazy condition / 34：
Special maximally monotone multifunctions / VI：
The norm-dual of the space E × E* and BC-functions / 35：
Subclasses of the maximally monotone multifunctions / 36：
First application of Theorem 35.8: type (D) implies type (FP) / 37：
Tclb(E**), TCLBN(B*) and type (ED) / 38：
Second application of Theorem 35.8: type (ED) implies type (FPV) / 39：
Final applications of Theorem 35.8: type (ED) implies strong / 40：
Strong maximality and coercivity / 41：
Type (ED) implies type (ANA) and type (BR) / 42：
The closure of the range / 43：
The sum problem and the closure of the domain / 44：
The biconjugate of a maximum and TCLB(E**) / 45：
Maximally monotone multifunctions with convex graph / 46：
Possibly discontinuous positive linear operators / 47：
Subtler properties of subdifferentials / 48：
Saddle functions and type (ED) / 49：
The sum problem for general Banach spaces / VII：
Introductory comments / 50：
Voisei's theorem / 51：
Sums with normality maps / 52：
A theorem of Verona-Verona / 53：
Open problems / VIII：
Glossary of classes of multifunctions / IX：
A selection of results / X：
Referencess
Subject index
Symbol index
Introduction
The Hahn-Banach-Lagrange theorem and some consequences / I：
The Hahn-Banach-Lagrange theorem / 1：
10.

電子ブック
ＥＢ
10. Affine Density in Wavelet Analysis
Gitta Kutyniok, J.-M Morel, F. Takens, SpringerLink (Online service)
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2007
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Introduction / 1：
Irregular Wavelet and Gabor Frames / 1.1：
Density for Gabor Systems / 1.2：
Geometry of Time-Scale Indices / 1.3：
Overview of Main Results / 1.4：
Wavelet and Gabor Frames / 2：
Frame Theory / 2.1：
Wavelet Analysis / 2.2：
Time-Frequency Analysis / 2.3：
Amalgam Spaces / 2.4：
Weighted Affine Density / 3：
Definitions / 3.1：
Basic Properties / 3.2：
The Notion of Affine Density by Sun and Zhou / 3.3：
Comparison of Both Notions of Affine Density / 3.4：
Qualitative Density Conditions / 4：
Existence of an Upper Frame Bound / 4.1：
Existence of a Lower Frame Bound / 4.2：
Examples of Wavelet Systems / 4.3：
Density of Sequences in R+ / 4.4：
Affine Density and the Local Integrability Condition / 4.5：
Amalgam Spaces on R \ {0} / 4.5.1：
A Density Version of the Local Integrability Condition / 4.5.2：
A Characterization of Wavelet Parseval Frames / 4.5.3：
Quantitative Density Conditions / 5：
Outline and Comparison with Previous Work / 5.1：
Density of Product Sequences / 5.2：
A Fundamental Relationship / 5.3：
The Nyquist Phenomenon / 5.4：
Sufficient Density Conditions for Wavelet Frames / 5.5：
Existence of Special Weight Functions / 5.6：
Co-Affine Systems / 5.7：
Homogeneous Approximation Property / 6：
Amalgam Spaces and the Continuous Wavelet Transform / 6.1：
The Basic Class B[subscript 0] / 6.2：
The Homogeneous Approximation Property for Wavelet Frames / 6.3：
The Comparison Theorem for Wavelet Frames / 6.4：
Density Results for Wavelet Schauder Bases / 6.5：
Weighted Beurling Density and Shift-Invariant Gabor Systems / 7：
Motivation and Outline of Chapter / 7.1：
Weighted Beurling Density / 7.2：
Littlewood-Paley Type Inequalities / 7.3：
Equivalent Definition of Weighted Beurling Density / 7.4：
Beurling Density, Frame Bounds, and Gabor Generators / 7.5：
Shift-Invariant Gabor Systems / 7.6：
References
Index
Introduction / 1：
Irregular Wavelet and Gabor Frames / 1.1：
Density for Gabor Systems / 1.2：
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