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Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis

  • Daniel Alpay
  • Maria Elena Luna-Elizarrarás
  • Michael Shapiro
  • Daniele C. Struppa

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
    Pages 1-17
  3. Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
    Pages 19-30
  4. Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
    Pages 31-36
  5. Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
    Pages 37-61
  6. Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
    Pages 63-77
  7. Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
    Pages 79-95

About this book

Introduction

This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers, and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars, and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.

Keywords

Schur analysis bicomplex functional analysis bicomplex modules bicomplex numbers hyperbolic valued norm

Authors and affiliations

  • Daniel Alpay
    • 1
  • Maria Elena Luna-Elizarrarás
    • 2
  • Michael Shapiro
    • 3
  • Daniele C. Struppa
    • 4
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.Departamento de MatemáticasESFM-IPNMexico D.F.Mexico
  3. 3.Departamento de MatemáticasESFM-IPNMexico D.F.Mexico
  4. 4.Schmid college of Science and TechnologyChapman UniversityOrangeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-05110-9
  • Copyright Information The Author(s) 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-05109-3
  • Online ISBN 978-3-319-05110-9
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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