LEADER 04676nam 22006135 450 001 9910595037603321 005 20250407201221.0 010 $a3-031-07531-5 024 7 $a10.1007/978-3-031-07531-5 035 $a(CKB)5840000000091769 035 $a(MiAaPQ)EBC7102033 035 $a(Au-PeEL)EBL7102033 035 $a(PPN)264953711 035 $a(DE-He213)978-3-031-07531-5 035 $a(EXLCZ)995840000000091769 100 $a20220923d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRegular Functions of a Quaternionic Variable /$fby Graziano Gentili, Caterina Stoppato, Daniele C. Struppa 205 $a2nd ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (302 pages) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 311 08$a3-031-07530-7 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 1.Definitions and Basic Results -- 2.Regular Power Series -- 3.Zeros -- 4.Infinite Products -- 5.Singularities -- 6.Integral Representations -- 7.Maximum Modulus Theorem and Applications -- 8.Spherical Series and Differential -- 9.Fractional Transformations and the Unit Ball -- 10.Generalizations -- 11. Function Theory over Non-symmetric Slice Domains.-12. Applications -- Bibliography -- Index. 330 $aThis book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications. As in the case of other interesting quaternionic function theories, the original motivations were the richness of the theory of holomorphic functions of one complex variable and the fact that quaternions form the only associative real division algebra with a finite dimension n>2. (Slice) regular functions quickly showed particularly appealing features and developed into a full-fledged theory, while finding applications to outstanding problems from other areas of mathematics. For instance, this class of functions includes polynomials and power series. The nature of the zero sets of regular functions is particularly interesting and strictly linked to an articulate algebraic structure, which allows several types of series expansion and the study of singularities. Integral representation formulas enrich the theory and are fundamental to the construction of a noncommutative functional calculus. Regular functions have a particularly nice differential topology and are useful tools for the construction and classification of quaternionic orthogonal complex structures, where they compensate for the scarcity of conformal maps in dimension four. This second, expanded edition additionally covers a new branch of the theory: the study of regular functions whose domains are not axially symmetric. The volume is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general. From the reviews of the 1st edition: ?[The authors] document their own very recent theory of quaternionic regular functions, a development that parallels familiar complex function theory spectacularly well. This user-friendly primary source confirms that quaternionic calculus is not a dead end, and clearly answers a popular question regarding the analogy of complex function theory (complex analysis) with quarternionic variables, making it an excellent basis for a capstone course. Summing Up: Highly recommended. Upper-division undergraduates through professionals.? (D. V. Feldman, Choice, Vol. 51 (1), September, 2013)". 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aFunctions of complex variables 606 $aSequences (Mathematics) 606 $aFunctional analysis 606 $aFunctions of a Complex Variable 606 $aSequences, Series, Summability 606 $aFunctional Analysis 615 0$aFunctions of complex variables. 615 0$aSequences (Mathematics) 615 0$aFunctional analysis. 615 14$aFunctions of a Complex Variable. 615 24$aSequences, Series, Summability. 615 24$aFunctional Analysis. 676 $a515.98 700 $aGentili$b Graziano$053784 702 $aStoppato$b Caterina 702 $aStruppa$b Daniele Carlo$f1955- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910595037603321 996 $aRegular Functions of a Quaternionic Variable$92502695 997 $aUNINA