"Rational
hyperholomorphic functions in R4"
By
DANIEL ALPAY
(Ben-Gurion
University of the Negev, in the city of Beer-Sheva in Israel )
Abstract:
In the talk we will define rational functions in
the hyperholomorphic setting. Three equivalent
characterizations are presented: the first one in terms of quotient and
products, the second one in terms of realization and the last one in terms of
backward-shift invariance. These various notions are suitably defined in the hyperholomorphic setting. A key tool is the Cauchy-Kovalevskaya product of hyperholomorphic
functions. We also discuss a reproducing kernel Hilbert space which seems to be
the counterpart of the Arveson space of the ball, and
the associated de Branges-Rovnyak spaces.
Date:
Time: 15.40
Place: Mathematics Seminar Room, SA-141