# School of Mathematics

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## Analysis

Analysis is the study of spaces and functions which have a notion of "distance" which allows limiting processes to be studied. Analysis at Leeds centres around functional analysis and harmonic analysis, both in the abstract theory, and in applications to mathematical physics and engineering.

### In this section

**Matthew Daws**

I am interested in many aspects of what algebra meets analysis: principally Banach and operator algebras arising in abstract harmonic analysis, and related areas. I have recently become interested in "topological" quantum groups: using the framework of operator algebras to study quantum groups. Typical problems I study will originate as a (Banach) algebraic question, but will often need tools from operator algebras for their solution.

**Vladimir Kisil**

Operator and C*-algebras with symmetries, particularly algebra of convolutions and pseudodifferential operators on Lie groups and homogeneous spaces;

Functional calculus of operators and associated notions of (joint) spectrum of operators;

Hilbert spaces of analytic functions with reproducing kernels arising from group representations in complex and Clifford analysis;

Applications of coherent states, wavelet transform and group representations in quantum mechanics, combinatorics, etc.

**Jonathan Partington**

My research interests centre on operator theory and Banach spaces of analytic functions. These include very abstract questions about invariant subspaces, where tools from complex analysis have been found useful, and also the study of particular types of operator, such as Hankel, Toeplitz and composition operators. I am very interested in applications of operator theory, which include the study of linear semigroup systems, control theory and partial differential equations.

**Charles Read**

Operator theory, invariant subspaces, hypercyclicity. Banach algebras, ideals, amenability. **Nicholas Young** (Research professor)

Mathematical analysis, particularly operators on Hilbert space; complex analysis; H infinity control. Recent work, in collaboration with Jim Agler (UC San Diego) and John E. McCarthy (Washington University), is on the extension of some classical theorems of function theory to functions of two variables.

For further information on our research work please see our Group pages.

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