Geodesic
Holomorphic extension of CR-functions with singularities on a~hypersurface
Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 681-691.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\Omega$ be a Stein manifold of dimension $n\geqslant 2$, let $G$ be a domain which is relatively compact in $\Omega$ with $\Omega\setminus\overline G$ connected, and let $K\subset\overline G$ with $K=\widehat K_\Omega$. It is shown that any CR-function $f$ which is defined on $\Gamma=\partial G\setminus K$ extends holomorphically to $G\setminus K$. A local version of this assertion is also obtained. 
@article{IM2_1991_37_3_a10,
     author = {A. M. Kytmanov},
     title = {Holomorphic extension of {CR-functions} with singularities on a~hypersurface},
     journal = {Izvestiya. Mathematics },
     pages = {681--691},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a10/}
}
TY  - JOUR
AU  - A. M. Kytmanov
TI  - Holomorphic extension of CR-functions with singularities on a~hypersurface
JO  - Izvestiya. Mathematics 
PY  - 1991
SP  - 681
EP  - 691
VL  - 37
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a10/
LA  - en
ID  - IM2_1991_37_3_a10
ER  - 
%0 Journal Article
%A A. M. Kytmanov
%T Holomorphic extension of CR-functions with singularities on a~hypersurface
%J Izvestiya. Mathematics 
%D 1991
%P 681-691
%V 37
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a10/
%G en
%F IM2_1991_37_3_a10
A. M. Kytmanov. Holomorphic extension of CR-functions with singularities on a~hypersurface. Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 681-691. http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a10/

[1] Lupacciolu G., “A theorem on holomorphic extension of $CR$-functions”, Pasific J. Math., 124:1 (1986), 177–191 | MR | Zbl

[2] Lupacciolu G., “Holomorphic continuation in several complex variables”, Pasific J. Math., 128:1 (1987), 117–126 | MR | Zbl

[3] Laurent-Thiebaut C., “Sur l'extension des fonctions $CR$ dans une variete de Stein”, Ann. Math. Pura Appl., 150 (1988), 141–151 | DOI | MR | Zbl

[4] Stout E. L., Removable singularities for the boundary values of holomorphic functions, Preprint, Univ. Washington, 1988, 21 pp. | MR | Zbl

[5] Polking J. C., Wells R. O., Jr., “Boundary values of Dolbeault cohomology classes and generalized Bochner–Hartogs theorem”, Abh. Math. Sem. Univ. Hamburg, 47 (1978), 3–24 | DOI | MR | Zbl

[6] Chirka E. M., “Regulyarizatsiya i $\overline\partial$-gomotopiya na kompleksnom mnogoobrazii”, DAN SSSR, 244:2 (1979), 300–303 | MR | Zbl

[7] Khermander L., Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968 | MR

[8] Khenkin G. M., “Metod integralnykh predstavlenii v kompleksnom analize”, Itogi nauki i tekhniki. Sovremennye problemy matematiki (fundamentalnye napravleniya), 7, VINITI, M., 1985, 23–124 | MR

[9] Rosay J.-P., Stout E. L., “Rado's theorem for $CR$-functions”, Proc. Amer. Math. Soc., 106:4 (1989), 1017–1026 | DOI | MR | Zbl

[10] Chirka E. M., “Analiticheskoe predstavlenie $CR$-funktsii”, Matem. sb., 98:4 (1975), 591–623 | MR | Zbl

[11] Chirka E. M., “Potoki i nekotorye ikh primeneniya”, v kn.: Kharvi R., Golomorfnye tsepi i ikh granitsy, Mir, M., 1979, 122–154 | MR

[12] Kheiman U., Kennedi P., Subgarmonicheskie funktsii, Mir, M., 1980

[13] Henkin G. M., “Solutions des equations de Cauchy–Riemann tangentielles sur des varietes de Cauchy–Riemann $q$-concaves”, C.R. Acad. Sci. Ser. 1, 292:1 (1981), 27–30 | MR | Zbl

[14] Lupacciolu G., “Some global results on extension of $CR$-objects in complex manifolds”, Trans. Amer. Math. Soc., 1989 | MR

[15] Laurent-Thiebaut C., Leiterer J., “On the Hartogs–Bochner extension phenomenon for differential forms”, Mat. Ann., 284:1 (1989), 103–119 | DOI | MR | Zbl

[16] Kytmanov A. M., “O stiranii osobennostei integriruemykh $CR$-funktsii”, MaTeM. sb., 136:2 (1988), 178–186 | MR | Zbl

[17] Golovin V. D., Gomologii analiticheskikh puchkov i teoremy dvoistvennosti, Nauka, M., 1986 | MR

[18] Trepreau J. M., “Sur le prolongement holomorphe des fonctions $CR$ definies sur une hypersurface reelle de classe $C^2$ dans $\mathbf{C}^n$”, Invent. Math., 83 (1986), 583–592 | DOI | MR | Zbl

[19] Khenkin G. M., “Effekt Gartogsa–Bokhnera na $CR$-mnogoobraziyakh”, DAN SSSR, 274:3 (1984), 553–558 | MR | Zbl