*Programme leaders: Ph.P.J.E. Clément, S.M. Verduyn Lunel*

This programme focusses 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, nonselfadjoint problems and completeness, the analysis of nonexpansive maps, stochastic differential equations in Banach spaces, operator-valued multiplier theorems, noncommutative analysis, higher-order elliptic and parabolic equations.