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 operatortheoretical methods to analyze problems arising from concrete classes of integral, differential and difference equations. Both linear and nonlinear equations are studied, and the problems may have a finitedimensional or infinitedimensional 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 nondeterministic systems, applications and further development of the state space method, nonselfadjoint problems and completeness, the analysis of nonexpansive maps.
Status of the programme.
Many equations arising in physical and biological models can be written as initialvalue problems for ordinary differential equations in infinitedimensional 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 infinitedimensional dynamical systems (compare the work of Foias, Hale and Temam) which also requires a stronger interaction with operator theory.
