Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
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ISBN-13:
9783319051093
Veröffentl:
2014
Einband:
Paperback
Erscheinungsdatum:
04.04.2014
Seiten:
112
Autor:
Daniel Alpay
Gewicht:
184 g
Format:
235x155x7 mm
Serie:
SpringerBriefs in Mathematics
Sprache:
Englisch
Beschreibung:
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.
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
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.
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