University of Leeds, School of Mathematics

Graduate course in Analysis


Time: Tuesdays from {11 a.m. to 12 noon} and {1 p.m. to 2 p.m.}, from Tuesday, January 28th 2003 until Tuesday, May 6th 2003.
Place: Classroom D, School of Mathematics
Lecturer: Prof. J.R. Partington

The course will fall into two fairly independent halves:

1. An elementary introduction to wavelets.

Introduction. Lp spaces and Fourier transforms. The Haar wavelet. Band-limited functions and the sampling theorem. Riesz bases and frames. The windowed Fourier transform. The wavelet transform. What happens next. Handout 1 (PDF)

2. Operator theory

Introduction. The graph of an operator. Closed and closable operators. Semigroups. PDE examples. The gap metric. Shift-invariant subspaces and shift-invariant operators (in as much detail as time permits). Handout 2 (PDF)

Prerequisites: it would be helpful to have seen the Fourier transform, and to know what a Hilbert space is.


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