Coverart for item
The Resource Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource)

Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource)

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 Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac
Creator
Contributor
Author
Provider
Subject
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 real-dimension four, while almost simultaneously James Cockle introduced a commutative four-dimensional 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 four-dimensional 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 one-dimensional 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
Member of
http://library.link/vocab/creatorName
Luna-Elizarrarás, M. Elena
Image bit depth
0
LC call number
QA331-355
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 Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource)
Instantiates
Publication
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
10.1007/978-3-319-24868-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-24868-4
Label
Bicomplex Holomorphic Functions : The Algebra, Geometry and Analysis of Bicomplex Numbers, by M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac, (electronic resource)
Publication
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
10.1007/978-3-319-24868-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-24868-4

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