R. Michael Range

Holomorphic Functions and Integral Representations in Several Complex Variables (eBook, PDF)

• Format: PDF

Produktbeschreibung

The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 392
• Erscheinungstermin: 9. März 2013
• Englisch
• ISBN-13: 9781475719185
• Artikelnr.: 44176846

Inhaltsangabe

1: Elementary Local Properties of Holomorphic Functions. 2: Domains of
Holomorphy and Pseudoconvexity. 3: Differential Forms and Hermitian
Geometry. 4: Integral Representations in C^n. 5: The Levi Problem and the
Solution of __ on Strictly Pseudoconvex Domains. 6: Function Theory on
Domains of Holomorphy in C^n. 7: Topics in Function Theory on Strictly
Pseudoconvex Domains.

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I Elementary Local Properties of Holomorphic Functions.- II Domains of Holomorphy and Pseudoconvexity.- III Differential Forms and Hermitian Geometry.- IV Integral Representations in ?n.- V The Levi Problem and the Solution of ?? on Strictly Pseudoconvex Domains.- VI Function Theory on Domains of Holomorphy in ?n.- VII Topics in Function Theory on Strictly Pseudoconvex Domains.- Appendix A.- Appendix B.- Appendix C.- Glossary of Symbols and Notations.