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Book Review

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Book Information:

Author: Robert C. Gunning
Title: Introduction to holomorphic functions of several variables
Additional book information: Wadsworth & Brooks/Cole, vol. 1, Function theory, 202 pp. ISBN 0-534-13308-8; vol. 2, Local theory, 215 pp. ISBN 0-534-13309-6; vol. 3, Homological theory, 194 pp. ISBN 0-534-13310-X.

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

  • Aldo Andreotti and Edoardo Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 81–130. MR 0175148
  • Eric Bedford and John Erik Fornæss, Counterexamples to regularity for the complex Monge-Ampère equation, Invent. Math. 50 (1978/79), no. 2, 129–134. MR 517774, 10.1007/BF01390286
  • [BET] H. Behuke and P. Thullen, Theorie der funktionen mehrerer komplexer veränderlichen, Springer-Verlag, Berlin, 1934.
  • [BER] L. Bers, Introduction to several complex variables, New York Univ. Press, New York, 1964.
  • Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863
  • E. M. Čirka, The Lindelöf and Fatou theorems in 𝐶ⁿ, Mat. Sb. (N.S.) 92(134) (1973), 622–644, 648 (Russian). MR 0338415
  • Michael Commichau and Hans Grauert, Das formale Prinzip für kompakte komplexe Untermannigfaltigkeiten mit 1-positivem Normalenbündel, Ann. of Math. Stud., vol. 100, Princeton Univ. Press, Princeton, N.J., 1981, pp. 101–126 (German). MR 627752
  • [JPDA] J. D'Angelo, Finite-type conditions for real hypersurfaces in Cn, (S. G. Krantz, ed.), Lecture Notes in Math., vol. 168, Springer-Verlag, Berlin, 1987, pp. 83-102.
  • Klas Diederich and John Erik Fornaess, Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), no. 2, 129–141. MR 0437806
  • Klas Diederich and John Erik Fornaess, Pseudoconvex domains: an example with nontrivial Nebenhülle, Math. Ann. 225 (1977), no. 3, 275–292. MR 0430315
  • Mike J. Field, Several complex variables and complex manifolds. I, London Mathematical Society Lecture Note Series, vol. 65, Cambridge University Press, Cambridge-New York, 1982. MR 651517
  • 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
  • G. B. Folland and E. M. Stein, Estimates for the ∂_{𝑏} complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 0367477
  • John Erik Fornæss and Berit Stensønes, Lectures on counterexamples in several complex variables, Mathematical Notes, vol. 33, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1987. MR 895821
  • H. Grauert and K. Fritzsche, Several complex variables, Springer-Verlag, New York-Heidelberg, 1976. Translated from the German; Graduate Texts in Mathematics, Vol. 38. MR 0414912
  • Hans Grauert and Ingo Lieb, Das Ramirezsche Integral und die Lösung der Gleichung ∂𝑓=𝛼 im Bereich der beschränkten Formen, Rice Univ. Studies 56 (1970), no. 2, 29–50 (1971) (German). MR 0273057
  • Hans Grauert and Reinhold Remmert, Theory of Stein spaces, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 236, Springer-Verlag, Berlin-New York, 1979. Translated from the German by Alan Huckleberry. MR 580152
  • Hans Grauert and Reinhold Remmert, Coherent analytic sheaves, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 265, Springer-Verlag, Berlin, 1984. MR 755331
  • Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
  • G. M. Henkin, Integral representation of functions which are holomorphic in strictly pseudoconvex regions, and some applications, Mat. Sb. (N.S.) 78 (120) (1969), 611–632 (Russian). MR 0249660
  • M. Hervé, Several complex variables. Local theory, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1963. MR 0151632
  • Lars Hörmander, 𝐿² estimates and existence theorems for the ∂ operator, Acta Math. 113 (1965), 89–152. MR 0179443
  • Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
  • [KOW] S. Kobayashi and H. H. Wu, Complex analytic geometry, Birkhäuser, Boston, 1983.
  • [KOH] J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. I, Ann. of Math. (2) 78 (1963), 112-148; II, ibid. (2) 79 (1964), 450-472.
  • J. J. Kohn and L. Nirenberg, A pseudo-convex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265–268. MR 0330513
  • Steven G. Krantz, Function theory of several complex variables, John Wiley & Sons, Inc., New York, 1982. Pure and Applied Mathematics; A Wiley-Interscience Publication. MR 635928
  • [OSG] W. F. Osgood, Lehrbuch der Funktionenetheorie, II, Teubner, Leipzig, 1924.
  • Nils Øvrelid, Integral representation formulas and 𝐿^{𝑝}-estimates for the ∂-equation, Math. Scand. 29 (1971), 137–160. MR 0324073
  • Enrique Ramírez de Arellano, Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis, Math. Ann. 184 (1969/1970), 172–187 (German). MR 0269874
  • 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
  • R. Michael Range, An elementary integral solution operator for the Cauchy-Riemann equations on pseudoconvex domains in 𝐶ⁿ, Trans. Amer. Math. Soc. 274 (1982), no. 2, 809–816. MR 675081, 10.1090/S0002-9947-1982-0675081-4
  • H. L. Royden, Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66. Princeton Univ. Press, Princeton, N.J., 1971, pp. 369–383. MR 0288254
  • Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
  • Walter Rudin, Function theory in the unit ball of 𝐶ⁿ, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
  • Nessim Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), no. 3, 205–230 (French). MR 0385164
  • E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Mathematical Notes, No. 11. MR 0473215
  • E. M. Stein, Singular integrals and estimates for the Cauchy-Riemann equations, Bull. Amer. Math. Soc. 79 (1973), 440–445. MR 0315302, 10.1090/S0002-9904-1973-13205-7
  • John Wermer, Banach algebras and several complex variables, 2nd ed., Springer-Verlag, New York-Heidelberg, 1976. Graduate Texts in Mathematics, No. 35. MR 0394218

Review Information:

Reviewer: Steven G. Krantz
Journal: Bull. Amer. Math. Soc. 25 (1991), 205-215