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 L^{1} and L^{2} 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:

- Stephen Krantz,
__A Panorama of Harmonic Analysis__. The Carus Mathematical Monographs No. 27, The Mathematical Association of America, Washington, D.C., 1999. ISBN 0-88385-031-1 - H. Dym, H.P. McKean,
__Fourier Series and Integrals__. Probability and Mathematical Statistics: A Series of Monographs and Textbooks Vol. 14, Academic Press, Toronto, 1972. ISBN 0-12226-450-9

Other notes:

- The function plotter used in Keith's demonstration was programmed by Keith Taylor and can be found at http://math.usask.ca/~code (click on "Function Plotter").
- A note on the form of the Fourier transform.
- Keith's assignment for the audience.

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