Real Analysis with an Introduction to Wavelets and Applications (eBook)

Robert Gardner, Don Hong, Jianzhong Wang (Autoren)

eBook Download: PDF

2004 | 1. Auflage
392 Seiten
Elsevier Science (Verlag)
978-0-08-054031-3 (ISBN)

Infos

An in-depth look at real analysis and its applications, including an introduction to wavelet
analysis, a popular topic in applied real analysis. This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral,
harmonic analysis and wavelet theory with many associated applications.

*The text is relatively elementary at the start, but the level of difficulty steadily increases
*The book contains many clear, detailed examples, case studies and exercises
*Many real world applications relating to measure theory and pure analysis
*Introduction to wavelet analysis

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Real Analysis with an Introduction to Wavelets and Applications is an in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "e;applied real analysis"e;. This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral, harmonic analysis and wavelet theory with many associated applications. The text is relatively elementary at the start, but the level of difficulty steadily increases The book contains many clear, detailed examples, case studies and exercises Many real world applications relating to measure theory and pure analysis Introduction to wavelet analysis

Inhalt

Front Cover 1
Real Analysis with an Introduction to Wavelets and Applications 4
Copyright Page 5
Contents 8
Preface 14
Chapter I. Fundamentals 18
1 Elementary Set Theory 18
2 Relations and Orderings 23
3 Cardinality and Countability 30
4 The Topology of Rn 36
Chapter 2. Measure Theory 50
1 Classes of Sets 52
2 Measures on a Ring 56
3 Outer Measures and Lebesgue Measure 62
4 Measurable Functions 71
5 Convergence of Measurable Functions 78
Chapter 3. The Lebesgue integral 82
1 Riemann Integral and Lebesgue Integral 82
2 The General Lebesgue Integral 89
3 Convergence and Approximation of Lebesgue Integrals 94
4 Lebesgue Integrals in the Plane 100
Chapter 4. Special Topics of Lebesgue Integral and Applications 106
1 Differentiation and Integration 106
2 Mathematical Models for Probability 119
3 Convergence and Limit Theorems 126
Chapter 5. Vector Spaces, Hilbert Spaces, and the L2 Space 132
1 Groups, Fields, and Vector Spaces 132
2 Inner Product Spaces 142
3 The Space L2 148
4 Projections and Hilbert Space Isomorphisms 153
5 Banach Spaces 162
Chapter 6. Fourier Analysis 172
1 Fourier Series 173
2 Parseval's Formula 185
3 The Fourier Transform of Integrable Functions 193
4 Fourier Transforms of Square Integrable Functions 207
5 The Poisson Summation Formula 215
Chapter 7. Orthonormal Wavelet Bases 226
1 Haar Wavelet Basis 228
2 Multiresolution Analysis 236
3 Orthonormal Wavelets from MRA 243
4 Orthonormal Spline Wavelets 254
5 Fast Wavelet Transforms 265
6 Biorthogonal Wavelet Bases 277
Chapter 8. Compactly Supported Wavelets 288
1 Symbols of Orthonormal Scaling Functions 288
2 The Daubechies Scaling Functions 300
3 Computation of Daubechies Scaling Fimctions 309
4 Wavelet Packets 318
5 Compactly Supported Biorthogonal Wavelet Bases 325
Chapter 9. Wavelets In Signal Processing 332
1 Signals 332
2 Filters 341
3 Coding Signals by Wavelet Transform 354
4 Filter Banks 363
Appendix 370
Biliography 374
Index 378

Produkt-Details

• Erscheint lt. Verlag: 31.12.2004
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik
• ISBN-10: 0-08-054031-7 / 0080540317
• ISBN-13: 978-0-08-054031-3 / 9780080540313