caa a22 4500 606209999 CHVBK 20210128101031.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00032-014-0231-9 doi (NATIONALLICENCE)springer-10.1007/s00032-014-0231-9 Realizations of Slice Hyperholomorphic Generalized Contractive and Positive Functions [Elektronische Daten] [Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini] We introduce generalized Schur functions and generalized positive functions in the setting of slice hyperholomorphic functions and study their realizations in terms of associated reproducing kernel Pontryagin spaces. To this end, we also prove some results in quaternionic functional analysis like an invariant subspace theorem for contractions in a Pontryagin space. We also consider slice hyperholomorphic functions on the half space $${\mathbb{H}_{+}}$$ H + of quaternions with positive real parts and we study the Hardy space H 2 $${(\mathbb{H}_{+})}$$ ( H + ) and Blaschke products in this framework. Springer Basel, 2014 Schur functions nationallicence realization nationallicence reproducing kernels nationallicence slice hyperholomorphic functions nationallicence Hardy spaces nationallicence S-resolvent operators nationallicence Alpay Daniel Department of Mathematics, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel aut Colombo Fabrizio Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133, Milano, Italy aut Lewkowicz Izchak Department of electrical engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel aut Sabadini Irene Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133, Milano, Italy aut Milan Journal of Mathematics Springer Basel 83/1(2015-06-01), 91-144 1424-9286 83:1<91 2015 83 32 https://doi.org/10.1007/s00032-014-0231-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00032-014-0231-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alpay Daniel Department of Mathematics, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel aut NATIONALLICENCE 700 1- Colombo Fabrizio Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133, Milano, Italy aut NATIONALLICENCE 700 1- Lewkowicz Izchak Department of electrical engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel aut NATIONALLICENCE 700 1- Sabadini Irene Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133, Milano, Italy aut NATIONALLICENCE 773 0- Milan Journal of Mathematics Springer Basel 83/1(2015-06-01), 91-144 1424-9286 83:1<91 2015 83 32