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Titlebook: Geometric Function Theory; Explorations in Comp Steven G. Krantz Textbook 2006 Birkhäuser Boston 2006 Complex analysis.Green‘s function.Poi

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书目名称Geometric Function Theory
副标题Explorations in Comp
编辑Steven G. Krantz
视频video
概述Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research.Contains an extensive bibliography of both monographs an
丛书名称Cornerstones
图书封面Titlebook: Geometric Function Theory; Explorations in Comp Steven G. Krantz Textbook 2006 Birkhäuser Boston 2006 Complex analysis.Green‘s function.Poi
描述.Complex 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. 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
出版日期Textbook 2006
关键词Complex analysis; Green‘s function; Poisson kernel; Potential theory; Schwarz lemma; calculus; differentia
版次1
doihttps://doi.org/10.1007/0-8176-4440-7
isbn_ebook978-0-8176-4440-6Series ISSN 2197-182X Series E-ISSN 2197-1838
issn_series 2197-182X
copyrightBirkhäuser Boston 2006
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Gedächtnis ist gut und schlechtThe concept of normal family is an outgrowth of the standard technique for proving the Riemann mapping theorem. Recall that the mapping function is produced as the solution of a certain extremal problem, and showing that that extremal problem actually has a solution is a byproduct of a normal families argument.
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Symmetrieoperationen mit Strecken,Every smoothly bounded domain in the complex plane has a Green’s function. The Green’s function is fundamental to the Poisson integral, the theory of harmonic functions, and to the broad panorama of complex function theory.
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Variations on the Theme of the Schwarz LemmaThe Schwarz lemma is one of the simplest results in all of complex function theory. A direct application of the maximum principle, it is merely a statement about the rate of growth of holomorphic functions on the unit disk.
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Birkhäuser Boston 2006
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Geometric Function Theory978-0-8176-4440-6Series ISSN 2197-182X Series E-ISSN 2197-1838
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