Classical wavelet theory

Postgraduate course in Analysis
Second semester, 2009-2010

The course is now finished.


PROVISIONAL SYLLABUS

1. Introduction.
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.

BOOKS

Ingrid Daubechies, Ten lectures on wavelets, SIAM.
C.K. Chui, An introduction to wavelets, Academic Press.
Gerald Kaiser, A friendly guide to wavelets, Birkhäuser.

PRE-REQUISITES

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)


Jonathan Partington

Last updated April 29th 2010