Bicomplex Holomorphic Functions: The Algebra, Geometry and - download pdf or read online

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

The function of this ebook is to improve the rules of the idea of holomorphicity at the ring of bicomplex numbers. consequently, the focus is on expressing the similarities with, and adjustments from, the classical idea of 1 advanced variable. the result's an basic but finished creation to the algebra, geometry and research of bicomplex numbers.

Around the center of the 19th century, a number of mathematicians (the top recognized being Sir William Hamilton and Arthur Cayley) took an interest in learning quantity structures 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 genuine algebra, which used to be rediscovered in 1892 by means of Corrado Segre, who observed his parts as bicomplex numbers. the benefits of commutativity have been observed via the creation of 0 divisors, anything that for it slow dampened curiosity during this topic. lately, due mostly to the paintings of G.B. expense, there was a resurgence of curiosity within the learn of those numbers and, extra importantly, within the learn of features 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 actual algebra, it's priceless to consider it as a “complexification” of the sector of complex

numbers; from this attitude, the bicomplex algebra possesses the houses of a one-dimensional idea within 4 actual dimensions. Its wealthy research and leading edge geometry supply new principles and strength purposes in relativity and quantum mechanics alike.

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

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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

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