Téléchargez le livre : Bicomplex Holomorphic Functions

Bicomplex Holomorphic Functions

The Algebra, Geometry and Analysis of Bicomplex Numbers de

, , ,

Éditeur :

Birkhäuser


Collection :

Frontiers in Mathematics

Paru le : 2015-12-11

eBook Téléchargement , DRM LCP 🛈 DRM Adobe 🛈
Lecture en ligne (streaming)
58,01 €
Téléchargement immédiat
Dès validation de votre commande
Image Louise Reader présentation

Louise Reader

Lisez ce titre sur l'application Louise Reader.

badge apple Application Louise Reader
badge Android Application Louise Reader
Description



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 thatfor 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.
Pages
231 pages
Collection
Frontiers in Mathematics
Parution
2015-12-11
Marque
Birkhäuser
EAN papier
9783319248660
EAN PDF
9783319248684
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
23
Taille du fichier
2437 Ko
Prix
58,01 €

Suggestions personnalisées