BEN GURION UNIVERSITY OF THE NEGEV
            DEPARTMENT OF MATHEMATICS
 
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       Operator and System Theory Seminar
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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
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Victor Vinnikov   <vinnikov@cs.bgu.ac.il>