Codice QDD209 Titolo Slice Hyperholomorphic Schur Analysis Data 2015-04-21 Autore/i Alpay, D.; Colombo, F.; Sabadini, I. Link Download full text Abstract The purpose of this work is to define and study the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. There are at least two motivations for such a study, both having in the background the desire to replace the complex numbers by the quaternions. One motivation comes from the theory of linear systems and signal processing. Another motivation is to define new tools and problems in hypercomplex analysis inspired from the complex setting (for instance Nevanlinna-Pick interpolation and the characteristic operator functions). The monograph is divided in three parts: namely Classical Schur analysis, Quaternionic analysis, and Quaternionic Schur analysis. Several parts in the second and third part are original and appear in this work for the first time.