SpringerBriefs in Mathematics

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

Authors: Alpay, D., Luna-Elizarrarás, M.E., Shapiro, M., Struppa, D.C.

  • Offers a self-contained introduction to functional analysis with bicomplex scalars and will serve for many subsequent developments similar to those of classic functional analysis
  • Only book that introduces a new hyperbolic valued norm on bicomplex modules which is crucial in obtaining some of the most important results in the book
  • First book in which Schur analysis is introduced in the bicomplex context
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Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05110-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-05109-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

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.

Table of contents (6 chapters)

  • Bicomplex and Hyperbolic Numbers

    Alpay, Daniel (et al.)

    Pages 1-17

  • Bicomplex Functions and Matrices

    Alpay, Daniel (et al.)

    Pages 19-30

  • $$\mathbb B\mathbb C$$ -Modules

    Alpay, Daniel (et al.)

    Pages 31-36

  • Norms and Inner Products on $$\mathbb B\mathbb C$$ -Modules

    Alpay, Daniel (et al.)

    Pages 37-61

  • Linear Functionals and Linear Operators on $${\mathbb {B}}{\mathbb {C}}$$ -Modules

    Alpay, Daniel (et al.)

    Pages 63-77

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05110-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-05109-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-05110-9
DOI
10.1007/978-3-319-05110-9
Softcover ISBN
978-3-319-05109-3
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XV, 95
Number of Illustrations and Tables
3 illustrations in colour
Topics