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