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.

The research of the second programme leader, S.M. Verduyn Lunel, is supported by a NWO PIONIER grant for his project "Analysis, dynamical systems and applications".

Close cooperation exists with research groups in Atlanta, Bloomington, Adelaide, Helsinki, Pisa, Bordeaux, New Brunswick, Paris VI, Reims, St. Petersburg and Tel-Aviv.
Both on an individual basis and through participation within international projects.

In the Netherlands there is close interaction with Diekmann (UU), Keane (UvA - CWI) and Peletier (UL). Regarding specific applications there is close interaction with Bliek (Chemische Technologie, UvA), Curtain (Systeemtheorie, RUG), Hemker (Numerieke Wiskunde, UvA - CWI), Den Hollander (KUN) and Dewilde (Elektrotechniek, TUD).

Research staff (situation at Januuary 1,2007)

• Permanent staff
• Prof.dr. H. Bart (EUR)
• Prof.dr. Ph.P.J.E. Clement (UL)
• Dr. O. van Gaans (UL)
• Prof.dr. I. Gohberg (VUA)
• Prof.dr.ir. J. de Graaf (TUE)
• Dr. S.C. Hille (UL)
• Dr. M.F.E. de Jeu (UL)
• Prof.dr. M.A. Kaashoek (VUA)
• Dr. J. van Neerven (TUD)
• Prof.dr. B. de Pagter (TUD)
• Prof.dr. A.C.M. Ran (VUA)
• Dr. V. Rottschäfer (UL/CWI)
• Prof.dr.ir. J.H. van Schuppen (VUA/CWI)
• Dr. F. van Schagen (VUA)
• Prof.dr. J.M. Schumacher (UvT)
• Dr. G. Sweers (TUD)
• Prof.dr. S.M. Verduyn Lunel (UL)
• Post Docs
• Dr. B.A. van de Rotten (UL)
• Ph.D. students
• Ir. G.N.J.C. Bierkens (UL)
• T.S. Gerasimov MSc (TUD)
• Drs. S. ter Horst (VUA)
• Drs. H.J. Hupkes (UL)
• Ir. J. Maas (TUD-NWO)
• M. Muskulus, dipl.math. (UL-NWO)
• Drs. M. van der Schans (UL)
• Drs. D. Worm (UL)
• Drs. A.M. Würth (UvT)