000 03733nam a22005055i 4500
001 978-3-642-33871-7
003 DE-He213
005 20140220082856.0
007 cr nn 008mamaa
008 130125s2013 gw | s |||| 0|eng d
020 _a9783642338717
_9978-3-642-33871-7
024 7 _a10.1007/978-3-642-33871-7
_2doi
050 4 _aQA331-355
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.9
_223
100 1 _aGentili, Graziano.
_eauthor.
245 1 0 _aRegular Functions of a Quaternionic Variable
_h[electronic resource] /
_cby Graziano Gentili, Caterina Stoppato, Daniele C. Struppa.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXIX, 185 p. 4 illus., 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _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 and Applications -- Bibliography -- Index.
520 _aThe theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the international research community. At the same time, the theory has already developed sturdy foundations. The richness of the theory of the holomorphic functions of one complex variable and its wide variety of applications are a strong motivation for the study of its analogs in higher dimensions. In this respect, the four-dimensional case is particularly interesting due to its relevance in physics and its algebraic properties, as the quaternion forms the only associative real division algebra with a finite dimension n>2. Among other interesting function theories introduced in the quaternionic setting, that of (slice) regular functions shows particularly appealing features. For instance, this class of functions naturally includes polynomials and power series. The zero set of a slice regular function has an interesting structure, strictly linked to a multiplicative operation, and it allows the study of singularities. Integral representation formulas enrich the theory and they are a fundamental tool for one of the applications, the construction of a noncommutative functional calculus. The volume presents a state-of-the-art survey of the theory and a brief overview of its generalizations and applications. It is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aFunctions of complex variables.
650 0 _aSequences (Mathematics).
650 1 4 _aMathematics.
650 2 4 _aFunctions of a Complex Variable.
650 2 4 _aSequences, Series, Summability.
650 2 4 _aFunctional Analysis.
700 1 _aStoppato, Caterina.
_eauthor.
700 1 _aStruppa, Daniele C.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642338700
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-33871-7
912 _aZDB-2-SMA
999 _c97436
_d97436