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Table of contents

  1. Front Matter
    Pages i-xii
  2. Classical Schur Analysis

    1. Front Matter
      Pages 1-2
    2. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 3-21
    3. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 23-35
    4. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 37-47
  3. Quaternionic Analysis

    1. Front Matter
      Pages 49-50
    2. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 51-69
    3. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 71-115
    4. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 117-164
    5. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 165-194
  4. Quaternionic Schur Analysis

    1. Front Matter
      Pages 195-196
    2. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 197-240
    3. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 241-264
    4. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 265-307
    5. Daniel Alpay, Fabrizio Colombo, Irene Sabadini
      Pages 309-331
  5. Back Matter
    Pages 333-362

About this book

Introduction

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 The book includes previously unpublished results and provides the basis for new directions of research.

Keywords

Slice hyperholomorphic functions quaternions reproducing kernels reproducing kernel spaces analytic functions linear operators linear systems interpolation problems indefinite inner product spaces Krein and Pontryagin spaces

Authors and affiliations

  • Daniel Alpay
    • 1
  • Fabrizio Colombo
    • 2
  • Irene Sabadini
    • 3
  1. 1.Chapman UniversityDepartment of Mathematics OrangeUSA
  2. 2.Dipartimento di MatematicaPolitecnico di Milano MilanoItaly
  3. 3.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42514-6
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-42513-9
  • Online ISBN 978-3-319-42514-6
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site