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ISSN 1088-6850(e) ISSN 0002-9947(p)

Extension and approximation of CR functions on tube manifolds

Author(s): André Boivin; Roman Dwilewicz
Journal: Trans. Amer. Math. Soc. 350 (1998), 1945-1956.
MSC (1991): Primary 32C16; Secondary 32D10, 32D15
MathSciNet review: 1443864
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Abstract: A complete generalization of the classical Bochner theorem for infinite tubes is given.

References:

[AH1]: R.A. Airapetjan and G.M. Henkin, Analytic continuation of CR-functions through the ``edge of the wedge", Soviet Math. Dokl. 24 (1981), 128 - 132. MR 82k:32039
[AH2]: R.A. Airapetjan and G.M. Henkin, Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions, Russian Math. Surveys 39 (1984), no. 3, 41 - 118. MR 86b:32003
[AR]: N.I. Ahiezer and L.I. Ronkin, Separately analytic functions of several variables, and ``edge of the wedge" theorems, Russian Math. Surveys 28 (1973), no. 3, 27 - 44. MR 54:7847
[BT]: M. S. Baouendi and F. Trèves, A microlocal version of Bochner's tube theorem, Indiana Univ. Math. J. 31 (1982), 885 - 895. MR 84b:35025
[Bo]: S. Bochner, A theorem on analytic continuation of functions in several variables, Ann.of Math. 39 (1938), 14 - 19.
[BM]: S. Bochner and W.T. Martin, Several Complex Variables, Princeton University Press, Princeton, N.J. (1948). MR 10:366a
[Bogg]: A. Boggess, CR Manifolds and the Tangential Cauchy-Riemann Equations, CRC Press, Studies in Advanced Mathematics (1991). MR 94e:32035
[Bogo]: N. N. Bogolyubov, Introduction to the Theory of Quantized Fields, GITTL, Moscow (1957), English translation, Interscience, New York, 1959. MR 20:5047; MR 22:1349
[BD]: A. Boivin and R. Dwilewicz, Holomorphic approximation of CR functions on tubular submanifolds of ${\mathbb{C}}^{2}$ , Annales Polonici Math. 55 (1991), 11 - 18. MR 93b:32017
[DG]: R. Dwilewicz and P.M. Gauthier, Global holomorphic approximations of CR functions on CR manifolds, Complex Variables 4 (1985), 377 - 391. MR 88b:32041
[DH]: R. Dwilewicz and C. D. Hill, The normal type function for CR manifolds, preprint.
[E]: H. Epstein, Generalization of the ``edge-of-the-wedge" theorem, J. Mathematical Phys. 1 (1960), 524 - 531. MR 22:10626
[H]: L. Hörmander, An Introduction to Complex Analysis in Several Variables (Third Ed.), North-Holland Mathematical Library 7 (1989). MR 91a:32001
[Ka]: M. Kazlow, CR functions and tube manifolds, Trans. Amer. Math. Soc. 255 (1979), 153 - 171. MR 80m:32001
[Ko]: H. Komatsu, A local version of Bochner's tube theorem, J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 19 (1972), 201 - 214. MR 47:5297
[M]: A.I. Markushevich, Theory of functions of a complex variable, Chelsea Publishing Company, New York, N.Y. (1985). MR 56:3258 (earlier printing)
[R]: W. Rudin, Lectures on the edge-of-the-wedge theorem, CBMS - AMS, No. 6, (1971). MR 46:9389
[Su]: H.J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171 - 188. MR 47:9666
[Tr]: J.M. Trépreau, Sur le prolongement holomorphe des fonctions C-R définies sur une hypersurface réelle de classe $C^{2}$ dans ${\mathbb{C}}^{n}$ , Invent. Math. 83 (1986), 583 - 592. MR 87f:32035
[Tu]: A. E. Tumanov, Extension of CR functions into a wedge from a manifold of finite type, Math. USSR Sbornik 64 (1989), 129 - 140. MR 89m:32037

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