Real Analysis with an Introduction to Wavelets and Applications


  • Don Hong, East Tennessee State University, Johnson City, TN
  • Jianzhong Wang, Sam Houston State University, Huntsville, TX
  • Robert Gardner, East Tennessee State University, Johnson City, TN

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.
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The book is intended for a one year senior undergraduate or beginning graduate course in RealAnalysis, Applied Analysis or Applied Mathematics found in mathematics, statistics, engineering and physics departments.


Book information

  • Published: December 2004
  • ISBN: 978-0-12-354861-0


"...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

Table of Contents

Fundamentals; Measure Theory; The Lebesgue Integral; Special Topics of Lebesgue Integral & Applications; Vector Spaces, Hilbert Spaces, and the L2 Space; Fourier Analysis; Orthonormal Wavelet Bases; Compactly Supported Wavelets; Wavelets in Signal Processing