BEN GURION UNIVERSITY OF THE NEGEV DEPARTMENT OF MATHEMATICS ================================== Operator and System Theory Seminar ================================== SPEAKER: Daniel Alpay, BGU TITLE: Schur functions and their realizations in the slice hyperholomorphic setting DATE: Monday, November 14, 2011 PLACE: Room -101, Mathematics Building, BGU TIME: 14:10 ABSTRACT: We start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space. This is joint work with Fabrizio Colombo and Irene Sabadini from Politecnico, Milan. For further announcements see <http://www.math.bgu.ac.il/~vinnikov/otseminar> For further information please contact: Daniel Alpay <dany@math.bgu.ac.il> , phone: 08-6461603 Victor Vinnikov <vinnikov@math.bgu.ac.il> , phone: 08-6461618 --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Victor Vinnikov <vinnikov@cs.bgu.ac.il>