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

DOI:
https://doi.org/10.1090/S0002-9947-98-02019-4

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. 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*, 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 dans*, 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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Additional Information

**André Boivin**

Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada

Email:
boivin@uwo.ca

**Roman Dwilewicz**

Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warsaw, Poland

Email:
rd@impan.gov.pl

DOI:
https://doi.org/10.1090/S0002-9947-98-02019-4

Keywords:
Tubular manifolds,
CR functions

Received by editor(s):
February 6, 1996

Received by editor(s) in revised form:
August 7, 1996

Additional Notes:
Research partially supported by NSERC grants

Article copyright:
© Copyright 1998
American Mathematical Society