In general, my research area would best suit
students who have studied (and enjoyed) courses on Hilbert Spaces and
The following topics would be suitable for a research student in pure mathematics.
* Banach spaces of analytic functions, including the classical Hardy spaces.
* Special classes of linear operators, particularly Hankel, Toeplitz and composition operators.
* Reproducing kernel Hilbert spaces.
* Invariant subspaces. Hypercyclicity.
* Semigroups of operators. Closed operators and the gap topology.
* Moment problems.
The remaining topics are rather more applied in nature, but are also areas of current research.
* Approximation, interpolation, signal processing.
* Wiener's generalized harmonic analysis, almost periodic signals and bounded power signals.
* Infinite-dimensional linear systems. Delay systems and fractional differential systems.
* Robust control. Worst-case identification. Spectral factorization.
* Controllability, observability, admissibility.
* Inverse problems for PDEs.
Publications. Postgraduate Research Brochure.
Last updated February 22nd 2010