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Cover: 9780817643393 | Geometric Function Theory | Explorations in Complex Analysis | Krantz
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Geometric Function Theory
Explorations in Complex Analysis
Buch von Steven G. Krantz
Sprache: Englisch

84,45 €*

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Beschreibung
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. 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.
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. 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.
Zusammenfassung

Complex variables is a precise, elegant, and captivating subject. Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research, with an understanding and explanation of their interrelations with other important parts of mathematics. 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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2005
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Cornerstones
Inhalt: xiii
314 S.
ISBN-13: 9780817643393
ISBN-10: 0817643397
Sprache: Englisch
Herstellernummer: 10979822
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Krantz, Steven G.
Hersteller: Birkh„user Boston
Birkhäuser Boston
Cornerstones
Maße: 241 x 160 x 24 mm
Von/Mit: Steven G. Krantz
Erscheinungsdatum: 20.09.2005
Gewicht: 0,664 kg
Artikel-ID: 102423516
Zusammenfassung

Complex variables is a precise, elegant, and captivating subject. Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research, with an understanding and explanation of their interrelations with other important parts of mathematics. 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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2005
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Cornerstones
Inhalt: xiii
314 S.
ISBN-13: 9780817643393
ISBN-10: 0817643397
Sprache: Englisch
Herstellernummer: 10979822
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Krantz, Steven G.
Hersteller: Birkh„user Boston
Birkhäuser Boston
Cornerstones
Maße: 241 x 160 x 24 mm
Von/Mit: Steven G. Krantz
Erscheinungsdatum: 20.09.2005
Gewicht: 0,664 kg
Artikel-ID: 102423516
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