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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: So-Chin Chen and Mei-Chi Shaw
Title: Partial differential equations in several complex variables
Additional book information: American Mathematical Society, Providence, RI, 2001, xii + 380 pp., ISBN 0-8218-1062-6, $49.00$

References [Enhancements On Off] (What's this?)

T. Aubin, Nonlinear Analysis on Manifolds, Monge-Ampère Equations, Springer-Verlag, New York, 1982. MR 0681859
G. B. Folland and J. J. Kohn, The Neumann Problem for the Cauchy-Riemann Complex, Princeton University Press, Princeton, 1972. MR 0461588
F. Hartogs, Zur Theorie der analytischen Functionen mehrener unabhangiger Veränderlichen insbesonder über die Darstellung derselben durch Reihen, welche nach Potenzen einter Veränderlichen fortschreiten, Math. Annalen 62(1906), 1-88.
L. Hörmander, $L^2$ estimates and existence theorems for the ${\overline{\partial}}$ operator, Acta Mathematica 113(1965), 89-152. MR 0179443
L. Hörmander, Introduction to Complex Analysis in Several Variables, North Holland, Amsterdam, 1973. MR 0344507
L. Hörmander, A history of existence theorems for the Cauchy-Riemann complex in $L^2$ spaces, Journal of Geometric Analysis 13(2003), to appear.
S. G. Krantz, Function Theory of Several Complex Variables, $2^{\rm nd}$ ed., American Mathematical Society, Providence, RI, 2001. MR 1846625
S. G. Krantz, What is several complex variables?, American Mathematical Monthly, 94(1987), 236-256. MR 0883291
S. G. Krantz, Partial Differential Equations and Complex Analysis, CRC Press, Boca Raton, FL, 1992. MR 1207812
R. M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer-Verlag, New York, 1986. MR 0847923

Review Information:

Reviewer: Steven G. Krantz
Affiliation: Washington University in St. Louis
Journal: Bull. Amer. Math. Soc. 40 (2003), 529-533
Published electronically: July 10, 2003
Review copyright: © Copyright 2003 American Mathematical Society