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Bulletin of the American Mathematical Society

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

Book Review

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Book Information:

Author: R. Michael Range
Title: Holomorphic functions and integral representations in several complex variables
Additional book information: Graduate Texts in Mathematics, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1986, xi + 386 pp., $49.50. ISBN 0-387-96259-x.

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

  • 1. Steven R. Bell, Biholomorphic mappings and the ∂-problem, Ann. of Math. (2) 114 (1981), no. 1, 103–113. MR 625347, 10.2307/1971379
  • 2. Steve Bell and Ewa Ligocka, A simplification and extension of Fefferman’s theorem on biholomorphic mappings, Invent. Math. 57 (1980), no. 3, 283–289. MR 568937, 10.1007/BF01418930
  • 3. David Catlin, Necessary conditions for subellipticity and hypoellipticity for the ∂-Neumann problem on pseudoconvex domains, Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979) Ann. of Math. Stud., vol. 100, Princeton Univ. Press, Princeton, N.J., 1981, pp. 93–100. MR 627751
  • 4. David Catlin, Boundary invariants of pseudoconvex domains, Ann. of Math. (2) 120 (1984), no. 3, 529–586. MR 769163, 10.2307/1971087
  • 5. John P. D’Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. (2) 115 (1982), no. 3, 615–637. MR 657241, 10.2307/2007015
  • 6. Klas Diederich and John E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. Math. (2) 107 (1978), no. 2, 371–384. MR 0477153
  • 7. Klas Diederich and Peter Pflug, Necessary conditions for hypoellipticity of the ∂-problem, Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979) Ann. of Math. Stud., vol. 100, Princeton Univ. Press, Princeton, N.J., 1981, pp. 151–154. MR 627755
  • 8. Reinhold Remmert, Funktionentheorie. I, Grundwissen Mathematik [Basic Knowledge in Mathematics], vol. 5, Springer-Verlag, Berlin, 1984 (German). MR 753290
  • 9. Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 0350069
  • 10. 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
  • 11. H. Grauert and R. Remmert, Analytische Stellenalgebren, Springer-Verlag, Berlin-New York, 1971 (German). Unter Mitarbeit von O. Riemenschneider; Die Grundlehren der mathematischen Wissenschaften, Band 176. MR 0316742
  • 12. 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
  • 13. 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
  • 14. P. C. Greiner and E. M. Stein, Estimates for the \overline∂-Neumann problem, Princeton University Press, Princeton, N.J., 1977. Mathematical Notes, No. 19. MR 0499319
  • 15. G. M. Henkin, Integral representation of functions in strongly pseudoconvex regions, and applications to the \overline∂-problem, Mat. Sb. (N.S.) 82 (124) (1970), 300–308 (Russian). MR 0265625
  • 16. Lars Hörmander, 𝐿² estimates and existence theorems for the ∂ operator, Acta Math. 113 (1965), 89–152. MR 0179443
  • 17. Lars Hörmander, An introduction to complex analysis in several variables, 3rd ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990. MR 1045639
  • 18. A. Hurwitz and R. Courant, Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, 1. Aufl, Springer-Verlag, Berlin, 1922.
  • 19. Klaus Jänich, Einführung in die Funktionentheorie, Springer-Verlag, Berlin-New York, 1977 (German). Hochschultext. MR 0473147
  • 20. J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. I, Ann. of Math. (2) 78 (1963), 112-148; II, Ann. of Math. (2) 79 (1964), 450-472.
  • 21. J. J. Kohn, Subellipticity of the ∂-Neumann problem on pseudo-convex domains: sufficient conditions, Acta Math. 142 (1979), no. 1-2, 79–122. MR 512213, 10.1007/BF02395058
  • 22. J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443–492. MR 0181815
  • 23. J. J. Kohn and L. Nirenberg, A pseudo-convex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265–268. MR 0330513
  • 24. Ingo Lieb, Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten. Beschränkte Lösungen, Math. Ann. 190 (1970/1971), 6–44 (German). MR 0283235
  • 25. Ingo Lieb and R. Michael Range, Integral representations and estimates in the theory of the \overline∂-Neumann problem, Ann. of Math. (2) 123 (1986), no. 2, 265–301. MR 835763, 10.2307/1971272
  • 26. Enrique Ramírez de Arellano, Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis, Math. Ann. 184 (1969/1970), 172–187 (German). MR 0269874
  • 27. Reinhold Remmert, Funktionentheorie. I, Grundwissen Mathematik [Basic Knowledge in Mathematics], vol. 5, Springer-Verlag, Berlin, 1984 (German). MR 753290
  • 28. S. M. Webster, Biholomorphic mappings and the Bergman kernel off the diagonal, Invent. Math. 51 (1979), no. 2, 155–169. MR 528021, 10.1007/BF01390226

Review Information:

Reviewer: Klas Diederich
Journal: Bull. Amer. Math. Soc. 20 (1989), 132-139
DOI: https://doi.org/10.1090/S0273-0979-1989-15730-3