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.

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 Includes supplementary material: sn.pub/extras

Inhalt

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.