Holomorphic functions and integral representations in several complex variables

R. Michael Range

This is an introductory text in several complex variables, using methods of integral representations. It begins with elementary local results, discusses basic new concepts of the multi-dimensional theory such as pseudoconvexity and holomorphic convexity, and leads up to complete proofs of fundamental global results, both classical and new. The use of integral representation techniques makes it possible to treat the subject with a minimum of prerequisites, and it has the further advantage that it uses the multivariable forms of theorem with which the students are already acquainted. This book also provides a systematic introduction to integral representation methods and their applications, including a simplified proof of C. Fefferman's famous mapping theorem.

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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.

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書名 Holomorphic functions and integral representations in several complex variables
著作者等 Range, R. Michael
Range R. Michael (State University of New York at Albany NY USA)
シリーズ名 Graduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1986
版表示 1st ed. 1986. Corr. 2nd printing 1998
ページ数 xviii, 386 p.
大きさ 25 cm
ISBN 354096259X
NCID BA00141061
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言語 英語
出版国 アメリカ合衆国

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