Slice Hyperholomorphic Schur Analysis. 1st ed. 2016

種類:

電子ブック

責任表示:

by Daniel Alpay, Fabrizio Colombo, Irene Sabadini

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016

著者名:

• Alpay, Daniel.
• Colombo, Fabrizio.
• Sabadini, Irene.
• SpringerLink (Online service)

シリーズ名:

Operator Theory: Advances and Applications ; 256

ISBN:

9783319425146 [3319425145]    

注記:

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 The book includes previously unpublished results and provides the basis for new directions of research.

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