September 15: Introduction to Wavelets

Keith gave a short history of the study of wavelets, mentioning the many sources of this field including, but not limited to, the theory of coherent states, quadrature mirror filtering in electrical engineering, geophysics (which gave us the term "wavelet"), the theory of square integrable representations, and classical harmonic analysis (including the Calderon reproducing formula).

A handout summarized some basic facts about Fourier analysis. In this seminar we will need some basic background in Fourier analysis, as well as a little bit of background in measure theory (particularly L1 and L2 spaces), norms, orthonormal bases and Hilbert space theory. For the non-mathematicians in the audience, either of the following two books will give a readable yet reasonably complete introduction to these topics:

Other notes:

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