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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. L*^{p} 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.

Last updated
May 7th 2005