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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.