naa a22 4500 510781446 CHVBK 20180411083248.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11854-013-0028-8 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0028-8 Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions [Elektronische Daten] [Daniel Alpay, Fabrizio Colombo, Irene Sabadini] We study reproducing kernel Hilbert and Pontryagin spaces of slice hyperholomorphic functions. These are analogs of the Hilbert spaces of analytic functions introduced by de Branges and Rovnyak. In the first part of the paper, we focus on the case of Hilbert spaces and introduce, in particular, a version of the Hardy space. Then we define Blaschke factors and Blaschke products and consider an interpolation problem. In the second part of the paper, we turn to the case of Pontryagin spaces. We first prove some results from the theory of Pontryagin spaces in the quaternionic setting and, in particular, a theorem of Shmulyan on densely defined contractive linear relations. We then study realizations of generalized Schur functions and of generalized Carathéodory functions. Hebrew University Magnes Press, 2013 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 Sabadini Irene Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133, Milano, Italy aut Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 87-125 0021-7670 121:1<87 2013 121 11854 https://doi.org/10.1007/s11854-013-0028-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0028-8 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- Sabadini Irene Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133, Milano, Italy aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 87-125 0021-7670 121:1<87 2013 121 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer