Alpay, D., Luna-Elizarrarás, M.E., Shapiro, M., Struppa, D.C.
2014, XV, 95 p. 3 illus. in color.
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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
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.