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.

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...

Table of Contents:

• 1. Bicomplex and hyperbolic numbers
• 2. Bicomplex functions and matrices
• 3. BC-modules
• 4. Norms and inner products on BC-modules
• 5. Linear functionals and linear operators on BC-modules
• 6. Schur analysis.