Geodesic
On holomorphic continuation of integrable functions along finite families of complex lines in an $n$-circular domain
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 91-96.

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

This paper contains some results related to holomorphic extension of integrable functions defined on the boundary of $D\subset\mathbb C^n$, $n>1$ into this domain. We shall consider integrable functions with the property of holomorphic extension along complex lines. In the complex plane $\mathbb C$ the results about functions with such property are trivial. Therefore, our results are essentially multidimensional.
Keywords: integrable functions, holomorphic extension, Szegö kernel, complex lines.
Mots-clés : Poisson kernel 
@article{JSFU_2018_11_1_a12,
     author = {Bayram P. Otemuratov},
     title = {On holomorphic continuation of integrable functions along finite families of complex lines in an $n$-circular domain},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {91--96},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a12/}
}
TY  - JOUR
AU  - Bayram P. Otemuratov
TI  - On holomorphic continuation of integrable functions along finite families of complex lines in an $n$-circular domain
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2018
SP  - 91
EP  - 96
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a12/
LA  - en
ID  - JSFU_2018_11_1_a12
ER  - 
%0 Journal Article
%A Bayram P. Otemuratov
%T On holomorphic continuation of integrable functions along finite families of complex lines in an $n$-circular domain
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2018
%P 91-96
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a12/
%G en
%F JSFU_2018_11_1_a12
Bayram P. Otemuratov. On holomorphic continuation of integrable functions along finite families of complex lines in an $n$-circular domain. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 91-96. http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a12/

[1] B.P. Otemuratov, “On functions of class $L^p$ with a property of one-dimensional holomorphic extension”, Vestnik KrasGU. Ser. fiz. mat. nauki, 2006, no. 9, 95–100 (in Russian)

[2] B.P. Otemuratov, “On multidimensional theorems of Morera for integrable functions”, Uzb. mat. zh., 2009, no. 2, 112–119 (in Russian) | MR

[3] B.P. Otemuratov, “Some sets of complex lines of minimal dimension sufficient for holomorphic continuation of integrable functions”, Journal SFU. Mathematics and physics, 5:1 (2012), 97–106 (in Russian)

[4] J. Globevnik, “Small families of complex lines for testing holomorphic extendibility”, Amer. J. of Math., 2012, no. 6, 1473–1490 | DOI | MR

[5] A.M. Kytmanov, S.G. Myslivets, “Holomorphic extension of functions along finite families of complex straight lines in an $n$-circular domain”, Sib. Math. J., 57:4 (2016), 618–631 | DOI | MR

[6] L.A. Aizenberg, A.P. Yuzhakov, Integral representations and residues in multidimensional complex analysis, Nauka, Novosibirsk, 1979 (in Russian) | MR

[7] G.M. Henkin, Method of integral representations in complex analysis, Results of science technology. Modern problems of mathematics, 7, M., 1985 (in Russian) | MR

[8] I. Stein, G. Weis, Introduction to Fourier analysis on Euclidean spaces, Mir, M., 1974 (in Russian) | MR

[9] A.M. Kytmanov, Bochner-Martinelli integral and its applications, Nauka, Novosibirsk, 1992 (in Russian) | MR

[10] A.M. Kytmanov, S.G. Myslivets, “Higher-dimensional boundary analogs of the Morera theorem in problems of analytic continuation of functions”, J. Math. Sci., 120:6 (2004), 1842–1867 | DOI | MR