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001449885 001__ 1449885
001449885 003__ OCoLC
001449885 005__ 20230310004423.0
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001449885 020__ $$a9783031075315$$q(electronic bk.)
001449885 020__ $$a3031075315$$q(electronic bk.)
001449885 020__ $$z9783031075308
001449885 0247_ $$a10.1007/978-3-031-07531-5$$2doi
001449885 035__ $$aSP(OCoLC)1346156742
001449885 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dEBLCP$$dOCLCF$$dOCLCQ
001449885 049__ $$aISEA
001449885 050_4 $$aQA331.7
001449885 08204 $$a515/.98$$223/eng/20220928
001449885 1001_ $$aGentili, Graziano,$$eauthor.
001449885 24510 $$aRegular functions of a quaternionic variable /$$cGraziano Gentili, Caterina Stoppato, Daniele C. Struppa.
001449885 250__ $$aSecond edition.
001449885 264_1 $$aCham :$$bSpringer,$$c[2022]
001449885 264_4 $$c©2022
001449885 300__ $$a1 online resource (xxv, 285 pages) :$$billustrations (chiefly color).
001449885 336__ $$atext$$btxt$$2rdacontent
001449885 337__ $$acomputer$$bc$$2rdamedia
001449885 338__ $$aonline resource$$bcr$$2rdacarrier
001449885 4901_ $$aSpringer monographs in mathematics,$$x2196-9922
001449885 504__ $$aIncludes bibliographical references and index.
001449885 5050_ $$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.
001449885 506__ $$aAccess limited to authorized users.
001449885 520__ $$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)".
001449885 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed September 28, 2022).
001449885 650_0 $$aFunctions, Quaternion.
001449885 655_0 $$aElectronic books.
001449885 7001_ $$aStoppato, Caterina,$$eauthor.
001449885 7001_ $$aStruppa, Daniele Carlo,$$d1955-$$eauthor.
001449885 830_0 $$aSpringer monographs in mathematics.$$x2196-9922
001449885 852__ $$bebk
001449885 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-07531-5$$zOnline Access$$91397441.1
001449885 909CO $$ooai:library.usi.edu:1449885$$pGLOBAL_SET
001449885 980__ $$aBIB
001449885 980__ $$aEBOOK
001449885 982__ $$aEbook
001449885 983__ $$aOnline
001449885 994__ $$a92$$bISE