Slice Hyperholomorphic Schur Analysis

• Main Authors: Alpay, Daniel (Author), Colombo, Fabrizio (Author), Sabadini, Irene (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
• Series: Operator Theory: Advances and Applications, 256
• Subjects: Mathematics.; Functional analysis.; Functions of complex variables.; Operator theory.; Functions of a Complex Variable.; Functional Analysis.; Operator Theory.

This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic f...

Table of Contents:

• Part I: Classical Schur analysis
• Preliminaries
• Rational functions
• Schur analysis
• Part II: Quaternionic analysis
• Finite dimensional preliminaries
• Quaternionic functional analysis
• Slice hyperholomorphic functions
• Slice hyperholomorphic operator-valued functions
• Part III: Quaternionic Schur analysis
• Reproducing kernel spaces and realizations
• Rational slice hyperholomorphic functions
• First applications: scalar interpolation and first order discrete systems
• Interpolation: operator-valued case.