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Book Review

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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?)

  • [AUB] Thierry Aubin, Nonlinear analysis on manifolds. Monge-Ampère equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 252, Springer-Verlag, New York, 1982. MR 681859
  • [FOK] G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Annals of Mathematics Studies, No. 75. MR 0461588
  • [HAR] 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.
  • [HOR1] Lars Hörmander, 𝐿² estimates and existence theorems for the ∂ operator, Acta Math. 113 (1965), 89–152. MR 0179443, https://doi.org/10.1007/BF02391775
  • [HOR2] Lars Hörmander, An introduction to complex analysis in several variables, Second revised edition, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973. North-Holland Mathematical Library, Vol. 7. MR 0344507
  • [HOR3] L. Hörmander, A history of existence theorems for the Cauchy-Riemann complex in $L^2$ spaces, Journal of Geometric Analysis 13(2003), to appear.
  • [KRA1] Steven G. Krantz, Function theory of several complex variables, AMS Chelsea Publishing, Providence, RI, 2001. Reprint of the 1992 edition. MR 1846625
  • [KRA2] Steven G. Krantz, What is several complex variables?, Amer. Math. Monthly 94 (1987), no. 3, 236–256. MR 883291, https://doi.org/10.2307/2323391
  • [KRA3] Steven G. Krantz, Partial differential equations and complex analysis, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. Lecture notes prepared by Estela A. Gavosto and Marco M. Peloso. MR 1207812
  • [RAN] R. Michael Range, Holomorphic functions and integral representations in several complex variables, Graduate Texts in Mathematics, vol. 108, Springer-Verlag, New York, 1986. MR 847923

Review Information:

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