
Geometric Function Theory
Explorations in Complex Analysis
Steven G. Krantz - Collection Cornerstones
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
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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