Slice Hyperholomorphic Schur Analysis

Description

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 functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research. Front Matter....Pages i-xii Front Matter....Pages 1-2 Preliminaries....Pages 3-21 Rational Functions....Pages 23-35 Schur Analysis....Pages 37-47 Front Matter....Pages 49-50 Finite-dimensional Preliminaries....Pages 51-69 Quaternionic Functional Analysis....Pages 71-115 Slice Hyperholomorphic Functions....Pages 117-164 Operator-valued Slice Hyperholomorphic Functions....Pages 165-194 Front Matter....Pages 195-196 Reproducing Kernel Spaces and Realizations....Pages 197-240 Rational Slice Hyperholomorphic Functions....Pages 241-264 First Applications: Scalar Interpolation and First-order Discrete Systems....Pages 265-307 Interpolation: Operator-valued Case....Pages 309-331 Back Matter....Pages 333-362