Footnote:
Includes bibliographical references (p. 357-359) and index. - Description based on print version record
Description:
Fundamentals -- Measure theory -- The Lebesgue integral -- Special topics of Lebesgue integral and applications -- Vector spaces, Hilbert spaces, and the L2 space -- Fourier analysis -- Orthonormal wavelet bases -- Compactly supported wavelets -- Wavelets in signal processing
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