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Geometric Function Theory : Explorations in Complex Analysis / by Steven G. Krantz
(Cornerstones. ISSN:21971838)
版 | 1st ed. 2006. |
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出版者 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser |
出版年 | 2006 |
本文言語 | 英語 |
大きさ | XIII, 314 p : online resource |
著者標目 | *Krantz, Steven G author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Functions of complex variables LCSH:Harmonic analysis LCSH:Geometry, Differential LCSH:Differential equations LCSH:Potential theory (Mathematics) FREE:Analysis FREE:Functions of a Complex Variable FREE:Abstract Harmonic Analysis FREE:Differential Geometry FREE:Differential Equations FREE:Potential Theory |
一般注記 | Classical 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 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, 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 HTTP:URL=https://doi.org/10.1007/0-8176-4440-7 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9780817644406 |
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電子リソース |
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EB00231110 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000115924 |
ISBN | 9780817644406 |
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