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

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis by Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Springer International Publishing
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Author: Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa ISBN: 9783319051109
Publisher: Springer International Publishing Publication: March 19, 2014
Imprint: Springer Language: English
Author: Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
ISBN: 9783319051109
Publisher: Springer International Publishing
Publication: March 19, 2014
Imprint: Springer
Language: English

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.

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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.

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