M. Elena Luna-Elizarrarás,Michael Shapiro,Daniele C.'s Bicomplex Holomorphic Functions: The Algebra, Geometry and PDF

By M. Elena Luna-Elizarrarás,Michael Shapiro,Daniele C. Struppa,Adrian Vajiac

The function of this e-book is to increase the rules of the speculation of holomorphicity at the ring of bicomplex numbers. as a result, the focus is on expressing the similarities with, and modifications from, the classical idea of 1 complicated variable. the result's an simple but finished creation to the algebra, geometry and research of bicomplex numbers.

Around the center of the 19th century, numerous mathematicians (the top recognized being Sir William Hamilton and Arthur Cayley) got interested in learning quantity platforms that prolonged the sector of advanced numbers. Hamilton famously brought the quaternions, a skew box in real-dimension 4, whereas nearly at the same time James Cockle brought a commutative 4-dimensional actual algebra, which used to be rediscovered in 1892 by way of Corrado Segre, who pointed out his components as bicomplex numbers. some great benefits of commutativity have been observed by way of the advent of 0 divisors, anything that for some time dampened curiosity during this topic. in recent times, due principally to the paintings of G.B. rate, there was a resurgence of curiosity within the examine of those numbers and, extra importantly, within the examine of services outlined at the ring of bicomplex numbers, which mimic the habit of holomorphic services of a posh variable.

While the algebra of bicomplex numbers is a 4-dimensional genuine algebra, it truly is beneficial to consider it as a “complexification” of the sector of complex

numbers; from this angle, the bicomplex algebra possesses the houses of a one-dimensional concept within 4 genuine dimensions. Its wealthy research and cutting edge geometry supply new rules and capability purposes in relativity and quantum mechanics alike.

The booklet will attract researchers within the fields of advanced, hypercomplex and sensible research, in addition to undergraduate and graduate scholars with an curiosity in a single- or multidimensional complicated analysis.

Show description

Read or Download Bicomplex Holomorphic Functions: The Algebra, Geometry and Analysis of Bicomplex Numbers (Frontiers in Mathematics) PDF

Best calculus books

Mathematical Analysis: Foundations and Advanced Techniques by Mariano Giaquinta,Giuseppe Modica PDF

Mathematical research: Foundations and complex suggestions for features of numerous Variables builds upon the elemental principles and strategies of differential and fundamental calculus for services of numerous variables, as defined in an past introductory quantity. The presentation is basically interested by the principles of degree and integration concept.

Download PDF by Emmanuel Fricain,Javad Mashreghi: The Theory of H(b) Spaces: Volume 1 (New Mathematical

An H(b) house is outlined as a suite of analytic features that are within the photograph of an operator. the idea of H(b) areas bridges classical matters: advanced research and operator idea, which makes it either beautiful and significant. the 1st quantity of this complete remedy is dedicated to the initial topics required to appreciate the root of H(b) areas, reminiscent of Hardy areas, Fourier research, quintessential illustration theorems, Carleson measures, Toeplitz and Hankel operators, a number of varieties of shift operators, and Clark measures.

Dajun Guo,V. Lakshmikantham,William F. Ames's Nonlinear Problems in Abstract Cones (Notes and reports in PDF

Notes and experiences in arithmetic in technology and Engineering, quantity five: Nonlinear difficulties in summary Cones offers the research of nonlinear difficulties in summary cones. This publication makes use of the speculation of cones coupled with the fastened element index to enquire optimistic mounted issues of assorted periods of nonlinear operators.

New PDF release: Vanishing Viscosity Method: Solutions to Nonlinear Systems

The ebook summarizes a number of mathematical points of the vanishing viscosity strategy and considers its purposes in learning dynamical structures reminiscent of dissipative platforms, hyperbolic conversion platforms and nonlinear dispersion platforms. together with unique study effects, the publication demonstrates tips on how to use such the way to resolve PDEs and is an important reference for mathematicians, physicists and engineers operating in nonlinear technology.

Additional info for Bicomplex Holomorphic Functions: The Algebra, Geometry and Analysis of Bicomplex Numbers (Frontiers in Mathematics)

Sample text

Download PDF sample

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

by Anthony

Rated 4.27 of 5 – based on 14 votes