000			03989nam a22005655i 4500
001			978-0-8176-4440-6
003			DE-He213
005			20180115171431.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780817644406 _9978-0-8176-4440-6
024	7		_a10.1007/0-8176-4440-7 _2doi
050		4	_aQA299.6-433
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515 _223
245	1	0	_aGeometric Function Theory _h[electronic resource] : _bExplorations in Complex Analysis / _cedited by Steven G. Krantz.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2006.
300			_aXIII, 314 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aCornerstones
505	0		_aClassical Function Theory -- Invariant Geometry -- Variations on the Theme of the Schwarz Lemma -- Normal Families -- The Riemann Mapping Theorem and Its Generalizations -- Boundary Regularity of Conformal Maps -- The Boundary Behavior of Holomorphic Functions -- Real and Harmonic Analysis -- The Cauchy-Riemann Equations -- The Green’s Function and the Poisson Kernel -- Harmonic Measure -- Conjugate Functions and the Hilbert Transform -- Wolff’s Proof of the Corona Theorem -- Algebraic Topics -- Automorphism Groups of Domains in the Plane -- Cousin Problems, Cohomology, and Sheaves.
520			_aComplex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme. This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis—and also to spark the interest of seasoned workers in the field—the book imparts a solid education both in complex analysis and in how modern mathematics works.
650		0	_aMathematics.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650		0	_aHarmonic analysis.
650		0	_aFunctions of complex variables.
650		0	_aPartial differential equations.
650		0	_aPotential theory (Mathematics).
650		0	_aDifferential geometry.
650	1	4	_aMathematics.
650	2	4	_aAnalysis.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aAbstract Harmonic Analysis.
650	2	4	_aDifferential Geometry.
650	2	4	_aPartial Differential Equations.
650	2	4	_aPotential Theory.
700	1		_aKrantz, Steven G. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817643393
830		0	_aCornerstones
856	4	0	_uhttp://dx.doi.org/10.1007/0-8176-4440-7
912			_aZDB-2-SMA
999			_c369872 _d369872