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Geometric Function Theory
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Geometric Function Theory

Geometric Function Theory

Explorations in Complex Analysis

Steven G. Krantz - Collection Cornerstones

314 pages, parution le 31/03/2005

Résumé

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.

L'auteur - Steven G. Krantz

Steven G. Krantz, currently Professor and Chairman of Mathematics at Washington University in St. Louis, earned his PhD at Princeton University and has taught at UCLA, Princeton University and Pennsylvania State University. He is the recipient of the UCLA Alumni Foundation Distinguished Teaching Award, the MAA's Chauvenet Prize, the MAA Beckenbach Book Award, and the Outstanding Academic Book Award of the Current Review of Academic Libraries. He has written numerous books including: "Function Theory of Several Complex Variables," "Real Analysis and Foundations," "The Geometry of Domains in Space" (with Harold R. Parks), "Function Theory of One Complex Variable" (with Robert E. Greene), "The Implicit Function Theorem" (with Harold Parks). "Complex Analysis: The Geometric Viewpoint," and" A Panorama of Harmonic Analysis" (both for the MAA). He is also the author of over one-hundred research articles.

Sommaire

  • Preface
  • Classical Function Theory
  • Real and Harmonic Analysis
  • Algebraic Topics
  • Bibliography
  • Index
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Steven G. Krantz
Collection Cornerstones
Parution 31/03/2005
Nb. de pages 314
Format 16 x 24
Couverture Relié
Poids 165g
Intérieur Noir et Blanc
EAN13 9780817643393
ISBN13 978-0-8176-4339-3

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