Real Analysis with an Introduction to Wavelets and Applications

ISBN-13: 9780123548610 / Angielski / Twarda / 2004 / 392 str.

Don Hong; Jianzhong Wang; Robert Gardner

Opis

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 "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

Recenzje

"...the wavelet treatment makes it attractive and gives it an edge over many texts." --David Ruch, Metropolitan State College

"The exercises I looked at were at a much more appropriate level than my current text. This book provides more exposition and more applications than traditional real analysis texts." --Doug Hardin, Vanderbilt University

Spis treści

Preface
1. Fundamentals
2. Measure Theory
3. The Lebesgue Integral
4. Special Topics of Lebesgue Integral & Applications
5. Vector Spaces, Hilbert Spaces, and the L2 Space
6. Fourier Analysis
7. Orthonormal Wavelet Bases
8. Compactly Supported Wavelets
9. Wavelets in Signal Processing
Appendix A: List of Symbols