LEADER 05171nam 22006735 450 001 9910300249403321 005 20220329213051.0 010 $a3-319-24868-5 024 7 $a10.1007/978-3-319-24868-4 035 $a(CKB)3710000000532704 035 $a(EBL)4189334 035 $a(SSID)ssj0001597180 035 $a(PQKBManifestationID)16297630 035 $a(PQKBTitleCode)TC0001597180 035 $a(PQKBWorkID)14886133 035 $a(PQKB)10764312 035 $a(DE-He213)978-3-319-24868-4 035 $a(MiAaPQ)EBC4189334 035 $a(PPN)190852844 035 $a(EXLCZ)993710000000532704 100 $a20151211d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBicomplex holomorphic functions $ethe algebra, geometry and analysis of bicomplex numbers /$fby M. Elena Luna-Elizarrarįs, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (231 p.) 225 1 $aFrontiers in Mathematics,$x1660-8046 300 $aDescription based upon print version of record. 311 $a3-319-24866-9 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 1.The Bicomplex Numbers -- 2.Algebraic Structures of the Set of Bicomplex Numbers -- 3.Geometry and Trigonometric Representations of Bicomplex -- 4.Lines and curves in BC -- 5.Limits and Continuity -- 6.Elementary Bicomplex Functions -- 7.Bicomplex Derivability and Differentiability -- 8.Some properties of bicomplex holomorphic functions -- 9.Second order complex and hyperbolic differential operators -- 10.Sequences and series of bicomplex functions -- 11.Integral formulas and theorems -- Bibliography. 330 $aThe purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers. Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in real-dimension four, while almost simultaneously James Cockle introduced a commutative four-dimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something that for a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable. While the algebra of bicomplex numbers is a four-dimensional real algebra, it is useful to think of it as a ?complexification? of the field of complex numbers; from this perspective, the bicomplex algebra possesses the properties of a one-dimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike. The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one- or multidimensional complex analysis. 410 0$aFrontiers in Mathematics,$x1660-8046 606 $aFunctions of complex variables 606 $aMathematical physics 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 615 0$aFunctions of complex variables. 615 0$aMathematical physics. 615 14$aFunctions of a Complex Variable. 615 24$aSeveral Complex Variables and Analytic Spaces. 615 24$aMathematical Applications in the Physical Sciences. 676 $a515.98 700 $aLuna-Elizarrarįs$b M. Elena$4aut$4http://id.loc.gov/vocabulary/relators/aut$01062363 702 $aShapiro$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aStruppa$b Daniele C$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVajiac$b Adrian$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300249403321 996 $aBicomplex Holomorphic Functions$92525162 997 $aUNINA