The Analysis Group
The research activities of the Analysis group are divided into three focus areas.
- Complex Analysis
- is a powerful tool in engineering, for example in hydrodynamics, signal analysis and control theory, and theoretical physics. These applications again lead to exciting new problems in complex analysis.
- Harmonic Analysis
- develops a signal into a collection of pure waves (harmonics), and then use this development to analyze the signal, including its compression and transmission.
- Functional Analysis and Non-commutative Geometry
- treats analysis in infinite dimensional vector spaces by utilising topological ideas. A linear map between two such spaces is called an operator. Classical examples of operators are differential and integral operators. It also includes C*-algebras and von Neumann algebras, and constitute the mathematical basis for quantum mechanics.