Slice Hyperholomorphic Schur Analysis

Daniel Alpay, Fabrizio Colombo, Irene Sabadini (Autoren)

Buch | Hardcover

XII, 362 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-42513-9 (ISBN)

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 The book includes previously unpublished results and provides the basis for new directions of research.

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.

"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)

“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)

Erscheinungsdatum	06.01.2017
Reihe/Serie	Operator Theory: Advances and Applications
Zusatzinfo	XII, 362 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Analytic Functions • Functional Analysis • Functions of a Complex Variable • indefinite inner product spaces • interpolation problems • Krein and Pontryagin spaces • Linear Operators • linear systems • mathematics and statistics • operator theory • quaternions • reproducing kernels • Reproducing kernel spaces • Slice hyperholomorphic functions
ISBN-10	3-319-42513-7 / 3319425137
ISBN-13	978-3-319-42513-9 / 9783319425139
Zustand	Neuware