Professor Jonathan Partington

My work is in the area of complex analysis and operator theory. Sometimes this is pure research in its own right, and sometimes it is applied to concrete problems, mostly in systems and control theory.

My research interests range widely, from pure mathematical topics to more applied themes.

On the pure side I am working with Banach spaces of analytic functions, including the classical Hardy spaces. Associated with these are special classes of linear operators, particularly Hankel, Toeplitz and composition operators. Other research topics concern interpolation in function spaces, invariant subspaces of operators and semigroups of operators.

On the applied side, I am interested in systems and control theory (particularly infinite-dimensional systems): here I have been working on delay systems and fractional systems, and also on questions of controllability, observability and admissibility. Analytic approximation methods have been used in identification problems, including inverse problems for partial differential equations. Finally, an old interest, namely rational approximation (model reduction), also resurfaces occasionally.

I am the author of four books on mathematics: An introduction to Hankel operators, Interpolation, Identification, and Sampling, Linear operators and linear systems and Modern approaches to the invariant-subspace problem.