Bulletin of the American Mathematical Society

MathSciNet review: 1567748
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Book Information:

Authors: John Erik Fornaess and Berit Stensønes
Title: Lectures on counterexamples in several complex variables
Additional book information: Mathematical Notes 33, Princeton University Press, Princeton, N. J., 1987, 247 pp., $22.50. ISBN 0-691-08456-4.

Patrick Ahern and Walter Rudin, Totally real embeddings of $S^3$ in $\textbf {C}^3$, Proc. Amer. Math. Soc. 94 (1985), no. 3, 460–462. MR 787894, DOI 10.1090/S0002-9939-1985-0787894-7

David E. Barrett, Irregularity of the Bergman projection on a smooth bounded domain in $\textbf {C}^{2}$, Ann. of Math. (2) 119 (1984), no. 2, 431–436. MR 740899, DOI 10.2307/2007045

G. Cœuré and J.-J. Loeb, A counterexample to the Serre problem with a bounded domain of $\textbf {C}^2$ as fiber, Ann. of Math. (2) 122 (1985), no. 2, 329–334. MR 808221, DOI 10.2307/1971305

Jean-Pierre Demailly, Un exemple de fibré holomorphe non de Stein à fibre $\textbf {C}^{2}$ ayant pour base le disque ou le plan, Invent. Math. 48 (1978), no. 3, 293–302 (French). MR 508989, DOI 10.1007/BF01390248

K. Diederich and J. E. Fornæss, Smooth, but not complex-analytic pluripolar sets, Manuscripta Math. 37 (1982), no. 1, 121–125. MR 649568, DOI 10.1007/BF01239949

Klas Diederich and John Erik Fornæss, A smooth curve in $\textbf {C}^{2}$ which is not a pluripolar set, Duke Math. J. 49 (1982), no. 4, 931–936. MR 683008, DOI 10.1215/S0012-7094-82-04944-4

Eva Kallin, A nonlocal function algebra, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 821–824. MR 152907, DOI 10.1073/pnas.49.6.821

Walter Rudin, Totally real Klein bottles in $\textbf {C}^{2}$, Proc. Amer. Math. Soc. 82 (1981), no. 4, 653–654. MR 614897, DOI 10.1090/S0002-9939-1981-0614897-1

Nessim Sibony, Sur la frontière de Shilov des domaines de $\textbf {C}^n$, Math. Ann. 273 (1985), no. 1, 115–121 (French, with English summary). MR 814198, DOI 10.1007/BF01455917

Nessim Sibony, Problème de la couronne pour des domaines pseudoconvexes à bord lisse, Ann. of Math. (2) 126 (1987), no. 3, 675–682 (French). MR 916722, DOI 10.2307/1971364

Yum Tong Siu, Holomorphic fiber bundles whose fibers are bounded Stein domains with zero first Betti number, Math. Ann. 219 (1976), no. 2, 171–192. MR 390303, DOI 10.1007/BF01351901

H. Skoda, Fibrés holomorphes à base et à fibre de Stein, Invent. Math. 43 (1977), no. 2, 97–107 (French). MR 508091, DOI 10.1007/BF01390000

Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR 0423083

[A. R] P. Ahern and W. Rudin, Totally real embeddings of S, Proc. Amer. Math. Soc. 94 (1985), 460-462. MR 0787894




[B] D. Barrett, Irregularity of the Bergman projection on a smooth bounded domain in C², Ann. of Math. (2) 119 (1984), 431-436. MR 740899




[C. L] G. Coeure and J. Loeb, A counterexample to the Serre Problem with a bounded domain of C, Ann. of Math. (2) 122 (1985), 329-334. MR 808221




[D] J. P. Demailly, Un example de fibre holomorphe non de Stein à fibre C, Invent. Math. 48 (1978), 293-302. MR 508989




[D. F] K. Diederich and J. E. Fornaess, Smooth but not complex analytic pluripolar sets, Manuscripta Math. 37 (1982), 121-125. MR 649568




[D. F] K. Diederich and J. E. Fornaess, A smooth curve in C, Duke Math. J. 49 (1982), 931-936. MR 683008




[K] E. Kallin, A non local function algebra, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 821-824. MR 152907




[R] W. Rudin, Totally real Klein bottles in C², Proc. Amer. Math. Soc. 82 (1981), 653-654. MR 614897




[Sil] N. Sibony, Sur la frontière de Shilov des domaines de C, Math. Ann. 273 (1985), 115-121. MR 814198




[Si2] N. Sibony, Problème de la couronne pour les domaines pseudoconvexes à bord lisse, Ann. of Math. (2) 126 (1987), 675-682. MR 916722




[Siu] Y. T. Siu, Holomorphic fiber bundles whose fibers are bounded Stein domains with zero first Betti number, Math. Ann. 219 (1976), 171-192 MR 390303




[Sk] H. Skoda, Fibres holomorphes à base et fibre de Stein, Invent. Math 43 (1977), 97-107. MR 508091




[St] E. L. Stout, The theory of uniform algebras, Bogden and Quigley, 1971. MR 423083