Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
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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.
complex variables, Schur analysis, Bicomplex Scalars
Algebra | Analysis
Alpay, D., Luna-Elizarrarás, M.E., Shapiro, M., Struppa, D.C., 2014. Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis, SpringerBriefs in Mathematics. Springer International Publishing, Cham.
This is the pre-print of a book that was later published by Springer in 2014. It may differ from the final, published version.