000			03091nam a22002897a 4500
003			OSt
005			20260609161237.0
008			260609b |||||||| |||| 00| 0 eng d
020			_a9783319248660
020			_a9783319248684
041			_aeng
082			_a515.9 LUN-B
100			_aLuna-Elizarraras, M. Elena _983559
245			_aBicomplex holomorphic functions : _bthe algebra, geometry and analysis of bicomplex numbers
260			_aCham, Heidelberg, New York : _bBirkhäuser, _c2015
300			_aviii, 231p.
440			_aFrontiers in Mathematics _983560
505			_aPresents a comprehensive study of the analysis and geometry of bicomplex numbers Offers a fundamental reference work for the field of bicomplex analysis Develops a solid foundation for potential new applications in relativity, dynamical systems and quantum mechanics
520			_aThe 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.
650			_aFunctions _xcomplex variables. _983561
700			_aShapiro, Michael. _983562
700			_aStruppa, Daniele C. _983563
700			_aVajiac, Adrian. _983564
856			_uhttps://doi.org/10.1007/978-3-319-24868-4
942			_cBK
999			_c200706 _d200706