Titlebook: Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis; Daniel Alpay,Maria Elena Luna-Elizarrarás,Daniele Boo

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2191-8198 s 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.978-3-319-05109-3978-3-319-05110-9Series ISSN 2191-8198 Series E-ISSN 2191-8201

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Book 2014nd 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

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Book 2014 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.

Pelago

Bicomplex and Hyperbolic Numbers,i of a bicomplex number which are not real valued: two of them are complex valued and one is hyperbolic valued. The notion of a positive hyperbolic number allows to introduce a partial order on the set of hyperbolic numbers which has far-reaching consequences in the theory of normed bicomplex module

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Alveoli

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The Lebedev Physics Institute SeriesIt turns out that hyperbolic valued norms are better compatible with the structure of bicomplex modules. In particular, the bicomplex valued inner products generate in a usual way: hyperbolic, not real, valued norms. As an example, the ring of biquaternions (complex quaternions) is treated as a bicomplex module.