Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Alpay, Daniel, Luna-Elizarrarás, Maria Elena, Shapiro, Michael, Struppa, Daniele C
Lenguaje:eng
Publicado: Springer 2014
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-05110-9
http://cds.cern.ch/record/1693446
_version_ 1780935930198097920
author Alpay, Daniel
Luna-Elizarrarás, Maria Elena
Shapiro, Michael
Struppa, Daniele C
author_facet Alpay, Daniel
Luna-Elizarrarás, Maria Elena
Shapiro, Michael
Struppa, Daniele C
author_sort Alpay, Daniel
collection CERN
description 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.
id cern-1693446
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2014
publisher Springer
record_format invenio
spelling cern-16934462021-04-21T21:04:35Zdoi:10.1007/978-3-319-05110-9http://cds.cern.ch/record/1693446engAlpay, DanielLuna-Elizarrarás, Maria ElenaShapiro, MichaelStruppa, Daniele CBasics of functional analysis with bicomplex scalars, and bicomplex Schur analysisMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:16934462014
spellingShingle Mathematical Physics and Mathematics
Alpay, Daniel
Luna-Elizarrarás, Maria Elena
Shapiro, Michael
Struppa, Daniele C
Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis
title Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis
title_full Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis
title_fullStr Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis
title_full_unstemmed Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis
title_short Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis
title_sort basics of functional analysis with bicomplex scalars, and bicomplex schur analysis
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-05110-9
http://cds.cern.ch/record/1693446
work_keys_str_mv AT alpaydaniel basicsoffunctionalanalysiswithbicomplexscalarsandbicomplexschuranalysis
AT lunaelizarrarasmariaelena basicsoffunctionalanalysiswithbicomplexscalarsandbicomplexschuranalysis
AT shapiromichael basicsoffunctionalanalysiswithbicomplexscalarsandbicomplexschuranalysis
AT struppadanielec basicsoffunctionalanalysiswithbicomplexscalarsandbicomplexschuranalysis

Ejemplares similares