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Book Information

Author(s): 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

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3.: D. Catlin, Necessary conditions of subellipticity and hypoellipticity for the $\bar \partial $-Neumann problem on pseudoconvex domains, Recent Developments in Several Complex Variables, Ann. of Math. Studies no. 100, 1981. MR 627751
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7.: K. Diederich and H. P. Pflug, Necessary conditions for hypoellipticity of the $\bar \partial $-problem, Recent Developments in Several Complex Variables, Ann. of Math. Studies no. 100, 1981, pp. 151-154. MR 627755
8.: K. Diederich and R. Remmert, Funktionentheorie. I, Springer-Verlag, Berlin-Heidelberg-New York, 1972. MR 753290
9.: C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. MR 350069
10.: H. Grauert and I. Lieb, Das Ramirezsche Integral und die Lösung der Gleichung $\bar \partial f=\alpha $ im Bereich der beschränkten Formen, Proc. Conf. Complex Analysis, Rice Univ., 1969, Rice Univ. Studies no. 56, 1970, pp. 29-50. MR 273057
11.: H. Grauert and R. Remmert, Analytische Stellenalgebren, Springer-Verlag, Berlin-Heidelberg-New York, 1971. MR 316742
12.: H. Grauert and R. Remmert, Theory of Stein spaces, Springer-Verlag, Berlin-Heidelberg, New York, 1979. MR 580152
13.: H. Grauert and R. Remmert, Coherent analytic sheaves, Springer-Verlag, Berlin-Heidelberg-New York, 1984. MR 755331
14.: P. C. Greiner and E. M. Stein, Estimates for the $øverline \partial $-Neumann problem, Princeton Univ. Press, Princeton, N.J., 1977. MR 499319
15.: G. M. Henkin, Integral representations of functions in strictly pseudoconvex domains and applications to the $øverline \partial $-problem, Math. Sb. 82 (1970), 300-308; English transl., Math. USSR Sb. 11 (1970), 273-281. MR 265625
16.: L. Hörmander, L, Acta Math. 113 (1965), 89-152. MR 179443
17.: L. Hörmander, An introduction to complex analysis in several variables, 2nd ed., North-Holland, Amsterdam-London, 1973. MR 1045639
18.: A. Hurwitz and R. Courant, Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, 1. Aufl, Springer-Verlag, Berlin, 1922.
19.: K. Jänich, Einführung in die Funktionentheorie, Springer-Verlag, Berlin-Heidelberg-New York, 1977. MR 473147
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 $\bar \partial $-Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979), 79-122. MR 512213
22.: J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443-492. MR 181815
23.: J. J. Kohn and L. Nirenberg, A pseudoconvex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265-268. MR 330513
24.: I. Lieb, Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudo-konvexen Gebieten, Math. Ann. 190 (1970), 6-44. MR 283235
25.: I. Lieb and R. M. Range, Integral representations and estimates in the theory of the $øverline\partial$-Neumann problem, Ann. of Math. (2) 123 (1986), 265-301. MR 835763
26.: E. Ramirez, Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis, Math. Ann. 184 (1970), 172-187. MR 269874
27.: R. Remmert, Funktionentheorie. I, Grundwissen Mathematik no. 5, Springer-Verlag, Berlin-Heidelberg-New York, 1984. MR 753290
28.: S. Webster, Biholomorphic mappings and the Bergman kernel of the diagonal, Invent. Math. 51 (1979), 155-169. MR 528021

Review Information:
Journal: Bull. Amer. Math. Soc. 20 (1989), 132-139.
DOI: 10.1090/S0273-0979-1989-15730-3
PII: S 0273-0979(1989)15730-3

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