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System and Operator Realizations of Analytic Functions |
The aim
of the workshop was to pay special attention to the analytic properties of
“transfer functions” which appear in different guises in different situations.
The Titchmarsh-Weyl coefficient from the theory of
Schrödinger operators is a well-known example. In the theory of boundary value
spaces there appear generalizations of the Titchmarsh-Weyl
coefficient in various forms. For instance in the theory of boundary triplets
there is a so-called Weyl (operator valued
holomorphic) function which carries all the spectral data of the boundary value
problem. An extension of the notion of boundary triplet leads to unbounded
multivalued Weyl functions. Parallel notions
appearing in system theory can be found, for instance, in the recent work by Arov and Staffans. During
the workshop there were 8 main one-hour lectures by Yury
Arlinskii, Malcolm Brown, Vladimir Derkach, Birgit Jacob, Hagen Neidhardt,
Mark Malamud, Arjan van der Schaft,
and Olof Staffans.
Furthermore there were 12 half-hour lectures. All lectures were concerned with
analytic objects from either boundary value problems involving boundary
triplets or relations, or from system theory. The workshop has generated joint
work between participants, which will be accessible in forthcoming
publications. The
schedule of the lectures provided a substantial opportunity for discussions and
joint work. The 25 participants of the workshop, including several PhD
students, came from Austria, Finland, Germany, Ireland, the Netherlands,
Poland, Ukraine, and the U.K. The
workshop at the Lorentz Center was sponsored by
several organizations: the Department of Mathematics of the TU Graz, the Johann
Bernoulli Institute for Mathematics and Computer Science of the University of
Groningen, the Department of Mathematics of the Jagiellonian
University in Krakow, and the Department of Mathematics and Statistics of the
University of Vaasa. We thank all these institutions for their support. The
conference at the Lorentz Center@Snellius with its
unique facilities was very much appreciated by the participants. We thank the
Lorentz Center for providing us with this opportunity
and their support; and also for helping us with getting the conference in
shape. We also want to thank the staff of the Lorentz Center
for their impressively smooth professionalism. In particular, we would like to
mention the contributions of Gerda Filippo and Mieke Schutte. [Back] |