2.1. Functional Analysis, Operator Theory, and Applications
Programme leaders: B. de Pagter, S.M. Verduyn Lunel
Description of the programme:
This programme focuses on operator-theoretical methods to analyze problems arising from concrete classes of integral, differential and difference equations. Both linear and non-linear equations are studied, and the problems may have a finite-dimensional or infinite-dimensional character. Typical for this programme is a strong interaction with dynamical systems, partial differential equations, probability theory and complex function theory. Important themes are the asymptotic behaviour of deterministic and of non-deterministic systems, applications and further development of the state space method, non-selfadjoint problems and completeness, the analysis of non-expansive maps.
Status of the programme.
Many equations arising in physical and biological models can be written as initial-value problems for ordinary differential equations in infinite-dimensional spaces. In analyzing such equations it is essential to have a thorough understanding of the corresponding linear (or possibly linearized) equation. Methods from operator theory play an important role in the mathematical analysis of such problems. On the international level there is an increasing interest in infinite-dimensional dynamical systems (compare the work of Foias, Hale and Temam) which also requires a stronger interaction with operator theory.