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Slice Hyperholomorphic Schur Analysis Softcover reprint of the original 1st ed. 2016 [Pehme köide]

  • Formaat: Paperback / softback, 362 pages, kõrgus x laius: 235x155 mm, kaal: 575 g, XII, 362 p., 1 Paperback / softback
  • Sari: Operator Theory: Advances and Applications 256
  • Ilmumisaeg: 04-Jul-2018
  • Kirjastus: Birkhauser Verlag AG
  • ISBN-10: 3319825976
  • ISBN-13: 9783319825977
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  • Formaat: Paperback / softback, 362 pages, kõrgus x laius: 235x155 mm, kaal: 575 g, XII, 362 p., 1 Paperback / softback
  • Sari: Operator Theory: Advances and Applications 256
  • Ilmumisaeg: 04-Jul-2018
  • Kirjastus: Birkhauser Verlag AG
  • ISBN-10: 3319825976
  • ISBN-13: 9783319825977

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 The book includes previously unpublished results and provides the basis for new directions of research.

Arvustused

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)

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.