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＜E-Book＞
Slice Hyperholomorphic Schur Analysis / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini
(Operator Theory: Advances and Applications. ISSN:22964878 ; 256)

Edition	1st ed. 2016.
Publisher	Cham : Springer International Publishing : Imprint: Birkhäuser
Year	2016
Language	English
Size	XII, 362 p : online resource
Authors	*Alpay, Daniel author Colombo, Fabrizio author Sabadini, Irene author SpringerLink (Online service)
Subjects	LCSH:Functions of complex variables LCSH:Functional analysis LCSH:Operator theory FREE:Functions of a Complex Variable FREE:Functional Analysis FREE:Operator Theory
Notes	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 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 The book includes previously unpublished results and provides the basis for new directions of research HTTP:URL=https://doi.org/10.1007/978-3-319-42514-6

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