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

• Main Authors: Alpay, Daniel (Author), Luna-Elizarrarás, Maria Elena (Author), Shapiro, Michael (Author), Struppa, Daniele C. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: SpringerBriefs in Mathematics,
• Subjects: Mathematics.; Functional analysis.; Functions of complex variables.; Operator theory.; System theory.; Functions of a Complex Variable.; Functional Analysis.; Operator Theory.; Systems Theory, Control.
• Physical Description: XV, 95 p. 3 illus. in color. online resource.
• ISBN: 9783319051109
• ISSN: 2191-8198

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.