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

Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael V Shapiro, Daniele Struppa

Research output: Book/ReportBookpeer-review


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.
Original languageEnglish
Place of PublicationCham
PublisherSpringer Cham
Number of pages95
ISBN (Electronic)3319051105, 9783319051109
ISBN (Print)3319051091, 9783319051093, 9783319051109
StatePublished - 2014

Publication series

NameSpringerBriefs in Mathematics
ISSN (Print)2191-8198
ISSN (Electronic)2191-8201


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


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