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1.

図書
図書
1. Numerical methods for bifurcation problems and large-scale dynamical systems
Eusebius Doedel, Laurette S. Tuckerman, editors
出版情報: New York : Springer, c2000  x, 471 p. ; 25 cm
シリーズ名: The IMA volumes in mathematics and its applications ; v. 119
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2.

図書
図書
2. Geometric numerical integration : structure-preserving algorithms for ordinary differential equations
Ernst Hairer, Christian Lubich, Gerhard Wanner
出版情報: Berlin ; Tokyo : Springer, c2002  xiii, 515 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; v. 31
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3.

図書
図書
3. An introduction to frames and Riesz bases
Ole Christensen
出版情報: Boston : Birkhäuser, c2003  xx, 440 p ; 24 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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目次情報: 続きを見る
Preface
Frames in Finite-dimensional Inner Product Spaces / 1：
Some basic facts about frames / 1.1：
Frame bounds and frame algorithms / 1.2：
Frames in C[superscript n] / 1.3：
The discrete Fourier transform / 1.4：
Pseudo-inverses and the singular value decomposition / 1.5：
Finite-dimensional function spaces / 1.6：
Exercises / 1.7：
Infinite-dimensional Vector Spaces and Sequences / 2：
Sequences / 2.1：
Banach spaces and Hilbert spaces / 2.2：
L[superscript 2] (R) and l[superscript 2] (N) / 2.3：
The Fourier transform / 2.4：
Operators on L[superscript 2] (R) / 2.5：
Bases / 2.6：
Bases in Banach spaces / 3.1：
Bessel sequences in Hilbert spaces / 3.2：
Bases and biorthogonal systems in H / 3.3：
Orthonormal bases / 3.4：
The Gram matrix / 3.5：
Riesz bases / 3.6：
Fourier series and Gabor bases / 3.7：
Wavelet bases / 3.8：
Bases and their Limitations / 3.9：
Gabor systems and the Balian-Low Theorem / 4.1：
Bases and wavelets / 4.2：
General shortcomings / 4.3：
Frames in Hilbert Spaces / 5：
Frames and their properties / 5.1：
Frame sequences / 5.2：
Frames and operators / 5.3：
Frames and bases / 5.4：
Characterization of frames / 5.5：
The dual frames / 5.6：
Tight frames / 5.7：
Continuous frames / 5.8：
Frames and signal processing / 5.9：
Frames versus Riesz Bases / 5.10：
Conditions for a frame being a Riesz basis / 6.1：
Riesz frames and near-Riesz bases / 6.2：
Frames containing a Riesz basis / 6.3：
A frame which does not contain a basis / 6.4：
A moment problem / 6.5：
Exercise / 6.6：
Frames of Translates / 7：
Sequences in R[superscript d] / 7.1：
Frames of translates / 7.2：
Frames of integer-translates / 7.3：
Irregular frames of translates / 7.4：
The sampling problem / 7.5：
Frames of exponentials / 7.6：
Gabor Frames in L[superscript 2] (R) / 7.7：
Continuous representations / 8.1：
Gabor frames / 8.2：
Necessary conditions / 8.3：
Sufficient conditions / 8.4：
The Wiener space W / 8.5：
Special functions / 8.6：
General shift-invariant systems / 8.7：
Selected Topics on Gabor Frames / 8.8：
Popular Gabor conditions / 9.1：
Representations of the Gabor frame operator and duality / 9.2：
The duals of a Gabor frame / 9.3：
The Zak transform / 9.4：
Tight Gabor frames / 9.5：
The lattice parameters / 9.6：
Irregular Gabor systems / 9.7：
Applications of Gabor frames / 9.8：
Wilson bases / 9.9：
Gabor Frames in l[superscript 2] (Z) / 9.10：
Translation and modulation on l[superscript 2] (Z) / 10.1：
Discrete Gabor systems through sampling / 10.2：
Gabor frames in C[superscript L] / 10.3：
Shift-invariant systems / 10.4：
Frames in l[superscript 2] (Z) and filter banks / 10.5：
General Wavelet Frames / 10.6：
The continuous wavelet transform / 11.1：
Sufficient and necessary conditions / 11.2：
Irregular wavelet frames / 11.3：
Oversampling of wavelet frames / 11.4：
Dyadic Wavelet Frames / 11.5：
Wavelet frames and their duals / 12.1：
Tight wavelet frames / 12.2：
Wavelet frame sets / 12.3：
Frames and multiresolution analysis / 12.4：
Frame Multiresolution Analysis / 12.5：
Frame multiresolution analysis / 13.1：
Relaxing the conditions / 13.2：
Construction of frames / 13.4：
Frames with two generators / 13.5：
Some limitations / 13.6：
Wavelet Frames via Extension Principles / 13.7：
The general setup / 14.1：
The unitary extension principle / 14.2：
Applications to B-splines I / 14.3：
The oblique extension principle / 14.4：
Fewer generators / 14.5：
Applications to B-splines II / 14.6：
Approximation orders / 14.7：
Construction of pairs of dual wavelet frames / 14.8：
Applications to B-splines III / 14.9：
Perturbation of Frames / 14.10：
A Paley-Wiener Theorem for frames / 15.1：
Compact perturbation / 15.2：
Perturbation of frame sequences / 15.3：
Perturbation of Gabor frames / 15.4：
Perturbation of wavelet frames / 15.5：
Perturbation of the Haar wavelet / 15.6：
Approximation of the Inverse Frame Operator / 15.7：
The first approach / 16.1：
A general method / 16.2：
Applications to Gabor frames / 16.3：
Integer oversampled Gabor frames / 16.4：
The finite section method / 16.5：
Expansions in Banach Spaces / 16.6：
Representations of locally compact groups / 17.1：
Feichtinger-Grochenig theory / 17.2：
Banach frames / 17.3：
p-frames / 17.4：
Gabor systems and wavelets in L[superscript p] (R) and related spaces / 17.5：
Appendix A / 17.6：
Normed vector spaces and inner product spaces / A.1：
Linear algebra / A.2：
Integration / A.3：
Some special normed vector spaces / A.4：
Operators on Banach spaces / A.5：
Operators on Hilbert spaces / A.6：
The pseudo-inverse / A.7：
Some special functions / A.8：
B-splines / A.9：
Notes / A.10：
List of symbols
References
Index
Preface
Frames in Finite-dimensional Inner Product Spaces / 1：
Some basic facts about frames / 1.1：
4.

図書
図書
4. Perturbation methods for differential equations
Bhimsen K. Shivamoggi
出版情報: Boston : Birkhäuser, c2003  xiv, 354 p. ; 24 cm
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5.

図書
図書
5. An introduction to minimax theorems and their applications to differential equations
by Maria do Rosário Grossinho and Stepan Agop Tersian
出版情報: Dordrecht : Kluwer Academic Publishers, c2001  xii, 269 p. ; 25 cm
シリーズ名: Nonconvex optimization and its applications ; v. 52
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6.

図書
図書
6. Introduction to the h-principle
Y. Eliashberg, N. Mishachev
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvii, 206 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 48
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目次情報: 続きを見る
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
Homotopy principle Open Diff $V$-invariant differential relations
Applications to closed manifolds
The homotopy principle in symplectic geometry: Symplectic and contact basics
Symplectic and contact structures on open manifolds
Symplectic and contact structures on closed manifolds
Embeddings into symplectic and contact manifolds
Microflexibility and holonomic $\mathcal{R}$-approximation
First applications of microflexibility
Microflexible $\mathfrak{U}$-invariant differential relations
Further applications to symplectic geometry
Convex integration: One-dimensional convex integration
Homotopy principle for ample differential relations
Directed immersions and embeddings
First order linear differential operators Nash-Kuiper theorem
Bibliography
Index
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
7.

図書
図書
7. Solution of ordinary differential equations by continuous groups
George Emanuel
出版情報: Boca Raton, FL : Chapman & Hall/CRC, 2001  220 p.
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目次情報: 続きを見る
Preface
Background / I：
Introduction / 1：
Continuous One-Parameter Groups-I / 2：
Group Concept / 2.1：
Infinitesimal Transformation / 2.2：
Global Group Equations / 2.3：
Problems / 2.4：
Method of Characteristics / 3：
Theory / 3.1：
Examples / 3.2：
Continuous One-Parameter Groups-II / 3.3：
Invariance / 4.1：
The Once-Extended Group / 4.2：
Higher-Order Extended Groups / 4.3：
Ordinary Differential Equations / 4.4：
First-Order ODEs / 5：
Invariance Under a One-Parameter Group / 5.1：
Canonical Coordinates / 5.2：
Special Procedures / 5.3：
Compendium / 5.4：
Higher-Order ODEs / 5.5：
Invariant Equations / 6.1：
Finding the Groups / 6.2：
System of First-Order ODEs / 6.3：
Second-Order ODEs / 6.4：
Classification of Two-Parameter Groups / 7.1：
Invariance and Canonical Coordinates / 7.2：
Appendices / 7.3：
Bibliography and References / A：
The Rotation Group / B：
Basic Relations / C：
Tables / D：
Answers to Selected Problems / E：
Preface
Background / I：
Introduction / 1：
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