My Research

My research interests include Automatic Continuity, Several Complex Variables, Hp spaces, and Reproducing Kernel Hilbert Spaces. In my research, I studied certain interpolation problems for analytic two-by-two matrix-valued functions on the unit disc.

The problem of designing controllers that are robust with respect to uncertainty leads to questions that are in the areas of Operator Theory and Several Complex Variables. One direction is the engineering problem of mu-synthesis, which has led to the study of certain inhomogeneous domains. Two such domains, the symmetrised bidisc and the tetrablock, are central in my research.

The mu-synthesis problem involves the construction of holomorphic matrix valued functions on the disc, subject to interpolation conditions and a boundedness condition. Using the properties of the tetrablock, I obtained a new solvability criterion for one such interpolation problem. The criterion uses the classical realisation formula and Hilbert space models in the sense of Agler to give an effective method for the construction of the required interpolating functions.

The research was joint work with Dr Zinaida Lykova and Prof. Nicholas Young. More information on the research can be found in our paper "A rich structure related to the construction of analytic matrix functions".

My Publications

D. C. Brown, Z. A. Lykova and N. J. Young, A rich structure related to the construction of analytic matrix functions, J. Funct. Anal. 272 (4) (2017), 1704-1754.

D. C. Brown, A rich structure related to the construction of holomorphic matrix functions, Thesis for admission to the degree of Doctor of Philosophy, Newcastle University, (2016). Link.

Talks given

Conferences attended