Current research interests - Jonathan R. Partington


In general, my research area would best suit students who have studied (and enjoyed) courses on Hilbert Spaces and Complex Analysis.
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.

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