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

This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It defines the notion of bicomplex modules and then develops the theory of linear functionals and linear operators on bicomplex modules.

List 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.

Summary

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.

Product details

• Authors: Danie Alpay, Daniel Alpay, Maria Elen Luna-Elizarrarás, Maria Elena Luna-Elizarrarás, Shapir, Michael Shapiro, Daniele C. Struppa
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 31.01.2014
• EAN: 9783319051093
• ISBN: 978-3-31-905109-3
• No. of pages: 95
• Dimensions: 177 mm x 246 mm x 8 mm
• Weight: 184 g
• Illustrations: XV, 95 p. 3 illus. in color.
• Series: SpringerBriefs in Mathematics; SpringerBriefs in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis