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Real analysis : with an introduction to wavelets and applications / Don Hong, Jianzhong Wang, Robert Gardner.
- Format:
- Book
- Language:
- English
- Subjects (All):
- Mathematical analysis.
- Wavelets (Mathematics).
- Physical Description:
- 1 online resource (387 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Amsterdam ; Boston : Elsevier Academic Press, c2005.
- Language Note:
- English
- Summary:
- An in-depth look at real analysis and its applications, including an introduction to waveletanalysis, 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
- Contents:
- Front Cover; Real Analysis with an Introduction to Wavelets and Applications; Copyright Page; Contents; Preface; Chapter I. Fundamentals; 1 Elementary Set Theory; 2 Relations and Orderings; 3 Cardinality and Countability; 4 The Topology of Rn; Chapter 2. Measure Theory; 1 Classes of Sets; 2 Measures on a Ring; 3 Outer Measures and Lebesgue Measure; 4 Measurable Functions; 5 Convergence of Measurable Functions; Chapter 3. The Lebesgue integral; 1 Riemann Integral and Lebesgue Integral; 2 The General Lebesgue Integral; 3 Convergence and Approximation of Lebesgue Integrals
- 4 Lebesgue Integrals in the PlaneChapter 4. Special Topics of Lebesgue Integral and Applications; 1 Differentiation and Integration; 2 Mathematical Models for Probability; 3 Convergence and Limit Theorems; Chapter 5. Vector Spaces, Hilbert Spaces, and the L2 Space; 1 Groups, Fields, and Vector Spaces; 2 Inner Product Spaces; 3 The Space L2; 4 Projections and Hilbert Space Isomorphisms; 5 Banach Spaces; Chapter 6. Fourier Analysis; 1 Fourier Series; 2 Parseval's Formula; 3 The Fourier Transform of Integrable Functions; 4 Fourier Transforms of Square Integrable Functions
- 5 The Poisson Summation FormulaChapter 7. Orthonormal Wavelet Bases; 1 Haar Wavelet Basis; 2 Multiresolution Analysis; 3 Orthonormal Wavelets from MRA; 4 Orthonormal Spline Wavelets; 5 Fast Wavelet Transforms; 6 Biorthogonal Wavelet Bases; Chapter 8. Compactly Supported Wavelets; 1 Symbols of Orthonormal Scaling Functions; 2 The Daubechies Scaling Functions; 3 Computation of Daubechies Scaling Fimctions; 4 Wavelet Packets; 5 Compactly Supported Biorthogonal Wavelet Bases; Chapter 9. Wavelets In Signal Processing; 1 Signals; 2 Filters; 3 Coding Signals by Wavelet Transform; 4 Filter Banks
- AppendixBiliography; Index
- Notes:
- Description based upon print version of record.
- Includes bibliographical references (p. 357-359) and index.
- ISBN:
- 1-281-02719-7
- 9786611027193
- 0-08-054031-7
- OCLC:
- 476079235
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