Extension and approximation of CR functions on tube manifolds

Boivin, André; Dwilewicz, Roman

doi:10.1090/S0002-9947-98-02019-4

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Extension and approximation
of CR functions on tube manifolds

Authors: André Boivin and 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 | References | Similar Articles | Additional Information

Abstract: A complete generalization of the classical Bochner theorem for infinite tubes is given.

[AH1] R. A. Aĭrapetjan and G. M. Henkin, Analytic continuation of CR-functions across the “edge of the wedge”, Dokl. Akad. Nauk SSSR 259 (1981), no. 4, 777–781 (Russian). MR 624846 (82k:32039)
[AH2] R. A. Aĭrapetyan and G. M. Khenkin, Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions, Uspekhi Mat. Nauk 39 (1984), no. 3(237), 39–106 (Russian). MR 747791 (86b:32003)
[AR] N. I. Ahiezer and L. I. Ronkin, Separately analytic functions of several variables, and “edge of the wedge” theorems, Uspehi Mat. Nauk 28 (1973), no. 3(171), 27–42 (Russian). MR 0419829 (54 #7847)
[BT] M. S. Baouendi and F. Trèves, A microlocal version of Bochner’s tube theorem, Indiana Univ. Math. J. 31 (1982), no. 6, 885–895. MR 674873 (84b:35025), http://dx.doi.org/10.1512/iumj.1982.31.31060
[Bo] S. Bochner, A theorem on analytic continuation of functions in several variables, Ann.of Math. 39 (1938), 14 - 19.
[BM] Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863 (10,366a)
[Bogg] Albert Boggess, CR manifolds and the tangential Cauchy-Riemann complex, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1991. MR 1211412 (94e:32035)
[Bogo] N. N. Bogolyubov and D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1957 (Russian). MR 0098590 (20 #5047)
N. N. Bogoliubov and D. V. Shirkov, Introduction to the theory of quantized fields, Authorized English edition. Revised and enlarged by the authors. Translated from the Russian by G. M. Volkoff. Interscience Monographs in Physics and Astronomy, Vol. III, Interscience Publishers, Inc., New York, 1959. MR 0110471 (22 #1349)
[BD] André Boivin and Roman Dwilewicz, Holomorphic approximation of CR functions on tubular submanifolds of 𝐶², Proceedings of the Tenth Conference on Analytic Functions (Szczyrk, 1990), 1991, pp. 11–18. MR 1141418 (93b:32017)
[DG] Roman Dwilewicz and P. M. Gauthier, Global holomorphic approximations of CR functions on CR manifolds, Complex Variables Theory Appl. 4 (1985), no. 4, 377–391. MR 858919 (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 0119868 (22 #10626)
[H] 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 (91a:32001)
[Ka] M. Kazlow, CR functions and tube manifolds, Trans. Amer. Math. Soc. 255 (1979), 153–171. MR 542875 (80m:32001), http://dx.doi.org/10.1090/S0002-9947-1979-0542875-5
[Ko] Hikosaburo Komatsu, A local version of Bochner’s tube theorem, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 19 (1972), 201–214. MR 0316749 (47 #5297)
[M] A. I. Markushevich, Theory of functions of a complex variable. Vol. I, II, III, Second English edition, Chelsea Publishing Co., New York, 1977. Translated and edited by Richard A. Silverman. MR 0444912 (56 #3258)
[R] Walter Rudin, Lectures on the edge-of-the-wedge theorem, American Mathematical Society, Providence, R.I., 1971. Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 6. MR 0310288 (46 #9389)
[Su] Héctor J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171–188. MR 0321133 (47 #9666), http://dx.doi.org/10.1090/S0002-9947-1973-0321133-2
[Tr] J.-M. Trépreau, Sur le prolongement holomorphe des fonctions C-R défines sur une hypersurface réelle de classe 𝐶² dans 𝐶ⁿ, Invent. Math. 83 (1986), no. 3, 583–592 (French). MR 827369 (87f:32035), http://dx.doi.org/10.1007/BF01394424
[Tu] J. J. Etayo and E. Martínez, Hyperbolic polygons and NEC groups, Math. Proc. Cambridge Philos. Soc. 104 (1988), no. 2, 261–272. MR 948911 (89m:32037), http://dx.doi.org/10.1017/S0305004100065439

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