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And what is important, the topics are presented with an explanation of their interaction with other important parts of mathematics.

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The presentations of the topics are clear and the text makes [for] very good reading; basic ideas of many concepts and proofs are carefully described, non-formal introductions to each chapter are very helpful, a rich collection of exercises is well composed and helps the student to understand the subject. The book under review leads the student to see what complex function theory has to offer and thereby gives him or her a taste of some of the areas of current research.

Geometric function theory: explorations in complex analysis

As such it is a welcome addition to the existing literature in complex function theory In this reviewer's opinion, the book can warmly be recommended both to experts and to a new generation of mathematicians. Geometric Function Theory. Explorations in Complex Analysis Sprache: Englisch. Keine Kommentare vorhanden Jetzt bewerten.

Kommentar verfassen. Produkt empfehlen. Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research Methodically designed with individual chapters containing a rich collection of exercises, examples, and Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren. Design and analysis of adaptive jet engine frame and thrust mounts.

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.

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Language English View all editions Prev Next edition 1 of 2. Author Krantz, Steven G.

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Abstract Harmonic Analysis. Differential Geometry. Functions of a Complex Variable. Partial Differential Equations. Potential Theory. Analytische meetkunde. Geometric function theory. Functions of complex variables. Summary "This methodologically 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.

Contents Pt. Classical function theory 1. Invariant geometry 2. Variations on the theme of the Schwarz Lemma 3. Normal families 4. The Riemann mapping theorem and its generalizations 5. Boundary regularity of conformal maps 6. The boundary behavior of holomorphic functions Pt. Real and harmonic analysis 7.

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The Cauchy-Riemann equations 8. The Green's function and the Poisson kernel 9. Harmonic measure Conjugate functions and the Hilbert transform Wolff's proof of the Corona theorem Pt. Algebraic topics Automorphism groups of domains in the plane Cousin problems, cohomology, and sheaves. Notes Formerly CIP. Includes bibliographical references p.

Steven George , Geometric function theory.