Slice Hyperholomorphic Schur Analysis

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 The book includes previously unpublished results and provides the basis for new directions of research.

List 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.

Report

"Purpose of the book is to define and study the counterpart of Schur functions and Schur analysis in the context of slice hyperholomorphic quaternionic functions. ... the book is an important contribution into each of the two theoriesthose of Schur analysis and of slice hyperholomorphic functions." (Michael Shapiro, Mathematical Reviews, September, 2017)

Product details

• Authors: Danie Alpay, Daniel Alpay, Fabrizi Colombo, Fabrizio Colombo, Irene Sabadini
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.2016
• EAN: 9783319425139
• ISBN: 978-3-31-942513-9
• No. of pages: 362
• Dimensions: 163 mm x 26 mm x 241 mm
• Weight: 717 g
• Illustrations: XII, 362 p.
• Series: Operator Theory: Advances and Applications; Birkhäuser; Operator Theory: Advances and Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Funktionalanalysis und Abwandlungen, Mathematics and Statistics, Functional Analysis, Functional analysis & transforms, Operator Theory, Functions of a Complex Variable, Functions of complex variables, interpolation problems, Krein and Pontryagin spaces, indefinite inner product spaces