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krantz s geometric function theory explorations complex analysis 2006

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Textbook in PDF format Complex analysis is a rich and textured subject. It is quite old, and its history is broad and deep. Yet the basic graduate course in complex variables has become rather cut and dried. The choice of topics, the order of the topics, and the overall ﬂavor of the presentation are strongly inﬂuenced by the need to prepare students for the qualifying exams. The qual-level course is designed to serve a limited purpose, and it does that but little more. The aim of the book is to expose the student to mathematics as it is practiced: as a synthesis of many diﬀerent areas, exhibiting particular ﬂavors and features that arise from that synthesis. The student who reads this book should be inspired to go further in the subject, to begin to explore the primary literature, and (one hopes) to think about his or her own research problems. With this book, the student and the advanced worker too are introduced to a rich tapestry of function theory as it interacts with other parts of mathematics. There is hardly any other analysis text that oﬀers such a variety and synthesis of mathematical topics. Contents. 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. 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. Automorphism Groups of Domains in the Plane. Cousin Problems, Cohomology, and Sheaves

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Krantz S. Geometric Function Theory. Explorations in Complex Analysis 2006.pdf 12.0 MB

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krantz s geometric function theory explorations complex analysis 2006

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