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The Resource Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena LunaElizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource)
Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena LunaElizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource)
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The item Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena LunaElizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena LunaElizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers. Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in realdimension four, while almost simultaneously James Cockle introduced a commutative fourdimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something that for a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable. While the algebra of bicomplex numbers is a fourdimensional real algebra, it is useful to think of it as a “complexification” of the field of complex < numbers; from this perspective, the bicomplex algebra possesses the properties of a onedimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike. The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one or multidimensional complex analysis
 Language
 eng
 Edition
 1st ed. 2015.
 Extent
 VIII, 231 p. 23 illus.
 Contents

 Introduction
 1.The Bicomplex Numbers
 2.Algebraic Structures of the Set of Bicomplex Numbers
 3.Geometry and Trigonometric Representations of Bicomplex
 4.Lines and curves in BC
 5.Limits and Continuity
 6.Elementary Bicomplex Functions
 7.Bicomplex Derivability and Differentiability
 8.Some properties of bicomplex holomorphic functions
 9.Second order complex and hyperbolic differential operators
 10.Sequences and series of bicomplex functions
 11.Integral formulas and theorems
 Bibliography
 Isbn
 9783319248684
 Label
 Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers
 Title
 Bicomplex Holomorphic Functions
 Title remainder
 The Algebra, Geometry and Analysis of Bicomplex Numbers
 Statement of responsibility
 by M. Elena LunaElizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac
 Language
 eng
 Summary
 The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers. Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in realdimension four, while almost simultaneously James Cockle introduced a commutative fourdimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something that for a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable. While the algebra of bicomplex numbers is a fourdimensional real algebra, it is useful to think of it as a “complexification” of the field of complex < numbers; from this perspective, the bicomplex algebra possesses the properties of a onedimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike. The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one or multidimensional complex analysis
 http://library.link/vocab/creatorName
 LunaElizarrarás, M. Elena
 Image bit depth
 0
 LC call number
 QA331355
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Shapiro, Michael.
 Struppa, Daniele C.
 Vajiac, Adrian.
 SpringerLink
 Series statement
 Frontiers in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Functions of complex variables
 Mathematical physics
 Mathematics
 Functions of a Complex Variable
 Several Complex Variables and Analytic Spaces
 Mathematical Applications in the Physical Sciences
 Label
 Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena LunaElizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  1.The Bicomplex Numbers  2.Algebraic Structures of the Set of Bicomplex Numbers  3.Geometry and Trigonometric Representations of Bicomplex  4.Lines and curves in BC  5.Limits and Continuity  6.Elementary Bicomplex Functions  7.Bicomplex Derivability and Differentiability  8.Some properties of bicomplex holomorphic functions  9.Second order complex and hyperbolic differential operators  10.Sequences and series of bicomplex functions  11.Integral formulas and theorems  Bibliography
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 VIII, 231 p. 23 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319248684
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319248684
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319248684
 Label
 Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena LunaElizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  1.The Bicomplex Numbers  2.Algebraic Structures of the Set of Bicomplex Numbers  3.Geometry and Trigonometric Representations of Bicomplex  4.Lines and curves in BC  5.Limits and Continuity  6.Elementary Bicomplex Functions  7.Bicomplex Derivability and Differentiability  8.Some properties of bicomplex holomorphic functions  9.Second order complex and hyperbolic differential operators  10.Sequences and series of bicomplex functions  11.Integral formulas and theorems  Bibliography
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 VIII, 231 p. 23 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319248684
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319248684
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319248684
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