語系:
繁體中文
English
說明(常見問題)
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Bicomplex Holomorphic Functions = Th...
~
Luna-Elizarrarás, M. Elena.
Bicomplex Holomorphic Functions = The Algebra, Geometry and Analysis of Bicomplex Numbers /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Bicomplex Holomorphic Functions/ by M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac.
其他題名:
The Algebra, Geometry and Analysis of Bicomplex Numbers /
作者:
Luna-Elizarrarás, M. Elena.
其他作者:
Shapiro, Michael.
面頁冊數:
VIII, 231 p. 23 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Functions of complex variables. -
電子資源:
https://doi.org/10.1007/978-3-319-24868-4
ISBN:
9783319248684
Bicomplex Holomorphic Functions = The Algebra, Geometry and Analysis of Bicomplex Numbers /
Luna-Elizarrarás, M. Elena.
Bicomplex Holomorphic Functions
The Algebra, Geometry and Analysis of Bicomplex Numbers /[electronic resource] :by M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac. - 1st ed. 2015. - VIII, 231 p. 23 illus.online resource. - Frontiers in Mathematics,1660-8046. - Frontiers in Mathematics,.
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.
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.
ISBN: 9783319248684
Standard No.: 10.1007/978-3-319-24868-4doiSubjects--Topical Terms:
528649
Functions of complex variables.
LC Class. No.: QA331-355
Dewey Class. No.: 515.9
Bicomplex Holomorphic Functions = The Algebra, Geometry and Analysis of Bicomplex Numbers /
LDR
:03919nam a22003975i 4500
001
963266
003
DE-He213
005
20200705122413.0
007
cr nn 008mamaa
008
201211s2015 gw | s |||| 0|eng d
020
$a
9783319248684
$9
978-3-319-24868-4
024
7
$a
10.1007/978-3-319-24868-4
$2
doi
035
$a
978-3-319-24868-4
050
4
$a
QA331-355
072
7
$a
PBKD
$2
bicssc
072
7
$a
MAT034000
$2
bisacsh
072
7
$a
PBKD
$2
thema
082
0 4
$a
515.9
$2
23
100
1
$a
Luna-Elizarrarás, M. Elena.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1258211
245
1 0
$a
Bicomplex Holomorphic Functions
$h
[electronic resource] :
$b
The Algebra, Geometry and Analysis of Bicomplex Numbers /
$c
by M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac.
250
$a
1st ed. 2015.
264
1
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Birkhäuser,
$c
2015.
300
$a
VIII, 231 p. 23 illus.
$b
online resource.
336
$a
text
$b
txt
$2
rdacontent
337
$a
computer
$b
c
$2
rdamedia
338
$a
online resource
$b
cr
$2
rdacarrier
347
$a
text file
$b
PDF
$2
rda
490
1
$a
Frontiers in Mathematics,
$x
1660-8046
505
0
$a
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.
520
$a
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.
650
0
$a
Functions of complex variables.
$3
528649
650
0
$a
Mathematical physics.
$3
527831
650
1 4
$a
Functions of a Complex Variable.
$3
672126
650
2 4
$a
Several Complex Variables and Analytic Spaces.
$3
672032
650
2 4
$a
Mathematical Applications in the Physical Sciences.
$3
786649
700
1
$a
Shapiro, Michael.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
898232
700
1
$a
Struppa, Daniele C.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
676849
700
1
$a
Vajiac, Adrian.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1258212
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9783319248660
776
0 8
$i
Printed edition:
$z
9783319248677
830
0
$a
Frontiers in Mathematics,
$x
1660-8046
$3
1258213
856
4 0
$u
https://doi.org/10.1007/978-3-319-24868-4
912
$a
ZDB-2-SMA
912
$a
ZDB-2-SXMS
950
$a
Mathematics and Statistics (SpringerNature-11649)
950
$a
Mathematics and Statistics (R0) (SpringerNature-43713)
筆 0 讀者評論
多媒體
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼[密碼必須為2種組合(英文和數字)及長度為10碼以上]
登入