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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 The book includes previously unpublished results and provides the basis for new directions of research.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.
Summary
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 The book includes previously unpublished results and provides the basis for new directions of research.
Additional text
“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)
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)
