Realizations of Slice Hyperholomorphic Generalized

Authors: Daniel Alpay Fabrizio Colombo Izchak Lewkowicz Irene Sabadini

Publish Date: 2014/12/05

Volume: 83, Issue: 1, Pages: 91-144

PDF Link

Abstract

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 mathbbH + of quaternions with positive real parts and we study the Hardy space H 2 mathbbH + and Blaschke products in this frameworkD Alpay thanks the Earl Katz family for endowing the chair which supported his research and the Binational Science Foundation Grant number 2010117 F Colombo and I Sabadini acknowledge the Center for Advanced Studies of the Mathematical Department of the BenGurion University of the Negev for the support and the kind hospitality during the period in which part of this paper has been written

Keywords: