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.
