Alpay / Colombo / Sabadini Slice Hyperholomorphic Schur Analysis

1. Auflage 2016
ISBN: 978-3-319-42514-6
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 256, 362 Seiten, eBook

Reihe: Operator Theory: Advances and Applications

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 The book includes previously unpublished results and provides the basis for new directions of research.

Zielgruppe

Research

Autoren/Hrsg.

Alpay, Daniel

Colombo, Fabrizio

Sabadini, Irene

Inhaltsverzeichnis

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.