"Rational hyperholomorphic functions in R4"
(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.
Place: Mathematics Seminar Room, SA-141