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Real Analysis with an Introduction to Wavelets and Applications

Don Hong, Jianzhong Wang and Robert Gardner
Elsevier Academic Press
Publication Date: 
Number of Pages: 
[Reviewed by
Mihaela Poplicher
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The book was written "with the student in mind" and intended mostly for students with a minimal background, both undergraduates and graduates. More precisely, students pursuing a master's degree in mathematics and taking a course called "Real Analysis," or "Applied Analysis," or "Introduction to Wavelets," could use (parts of) this book as a regular textbook, or as a reference.

The first few chapters of the book treat the "classical real analysis" topics: Fundamentals, Measure Theory, The Lebesgue Integral. They are followed by a few chapters of "applied analysis": Special Topics of Lebesgue Integral and Applications, Vector Spaces, Hilbert Spaces, and the Lp Space, Fourier Analysis and a few chapters dedicated to the introduction of wavelets and their applications: Orthonormal Wavelet Basis, Compactly Supported Wavelets, Wavelets in Signal Processing.

Each section ends with a number of exercises, most of which are not difficult and intended as practice problems for students. They are very well connected with the topics treated and many are applied in nature. I think these aspects make these exercises very appropriate for the audience for which the book is intended.

In short, this book will be very useful for any instructor teaching a master's level course and will be very well received by the students taking such a course.

Mihaela Poplicher is an assistant professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is

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