03147nam 22006015 450 991015544470332120251002143442.03-319-42514-510.1007/978-3-319-42514-6(CKB)4340000000024372(DE-He213)978-3-319-42514-6(MiAaPQ)EBC4768864(PPN)197455425(EXLCZ)99434000000002437220161210d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierSlice Hyperholomorphic Schur Analysis /by Daniel Alpay, Fabrizio Colombo, Irene Sabadini1st ed. 2016.Cham :Springer International Publishing :Imprint: Birkhäuser,2016.1 online resource (XII, 362 p.)Operator Theory: Advances and Applications,2296-4878 ;2563-319-42513-7 Includes bibliographical references and indexes.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 The book includes previously unpublished results and provides the basis for new directions of research.Operator Theory: Advances and Applications,2296-4878 ;256Functions of complex variablesFunctional analysisOperator theoryFunctions of a Complex VariableFunctional AnalysisOperator TheoryFunctions of complex variables.Functional analysis.Operator theory.Functions of a Complex Variable.Functional Analysis.Operator Theory.515.782Alpay Danielauthttp://id.loc.gov/vocabulary/relators/aut54298Colombo Fabrizioauthttp://id.loc.gov/vocabulary/relators/autSabadini Ireneauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910155444703321Slice Hyperholomorphic Schur Analysis2175766UNINA