Postgraduate course in Analysis
Second semester, 2009-2010
The course is now finished.
2. Review of Lp spaces and Fourier transforms.
3. The Haar wavelet.
4. Bandlimited functions and the sampling theorem.
5. Riesz bases and frames.
6. Windowed Fourier transforms.
7. The wavelet transform.
8. Multiresolution analysis.
9. Further wavelet constructions.
Ingrid Daubechies, Ten lectures on wavelets, SIAM.
C.K. Chui, An introduction to wavelets, Academic Press.
Gerald Kaiser, A friendly guide to wavelets, Birkhäuser.
It would help to have seen Lp spaces and Fourier transforms before. Also to know (roughly) what a Banach space and a Hilbert space are.
Notes for the course (now complete) (PDF)
Example Sheets 1 and 2 (PDF)
Last updated April 29th 2010