Schur analysis in the quaternionic setting

Presenter: Daniel Alpay, Ben-Gurion University of the Negev, Israel

Joint work with Fabrizo Colombo, Irene Sabadini, David Kimsey, Khaled Abuganem, Vladimir Bolotnikov

Schur analysis can be seen as a collection of problems associated to functions analytic and contractive in the open unit disk or with a real positive part there. It has deep implications in operator theory, linear systems, signal processing and related topics. Schur analysis has been considered in a variety of other settings (for instance in the setting of the poly-disk and of compact Riemann surfaces. In the first part of the talk we will give a brief survey of Schur analysis. In the second part of the talk we discuss Schur analysis in the setting of slice-hyperholomorphic functions. This leads to a number of new questions and notions in the quaternionic setting.