Geodesic
An analogue of the Hartogs lemma for $R$-analytic functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 196-200.

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The paper is devoted to the problem of $R$-analytic continuation of functions of several real variables which admit $R$-analytic continuation along parallel sections. We prove an analogue of the well-known Hartogs lemma for $R$-analytic functions.
Keywords: $R$-analytic functions, holomorphic functions, plurisubharmonic functions, Hartogs series.
Mots-clés : pluripolar sets 
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Alimardon A. Atamuratov; Djurabay K. Tishabaev; Takhir T. Tuychiev. An analogue of the Hartogs lemma for $R$-analytic functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 196-200. http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a5/

[1] A. Sadullaev, “Real analyticity of a $C^{\infty }$-germ at a origin”, Ann. Polon. Math., 2021 (Published online) | DOI | MR

[2] A.S. Sadullaev, E M. Chirka, “On continuation of functions with polar singularities”, Math. USSR-Sb., 60:2 (1988), 377–384 | DOI | MR | Zbl

[3] E.M. Chirka, “Rational approximations of holomorphic functions with singularities of finite order”, Math. USSR-Sb., 29:1 (1976), 123–138 | DOI | MR

[4] J. Bochnak, J. Siciak, “A characterization of analytic functions of several real variables”, Ann. Polon. Math., 123 (2019), 9–13 | DOI | MR | Zbl

[5] A. Sadullaev, “Rational approximation and pluripolar sets”, Math. USSR-Sb., 47:1 (1984), 91–113 | DOI | MR | Zbl

[6] A. Sadullaev, Holomorphic functions of several variables, Urgench State University Publishing Department, Urgench, 2005 (in Russian)

[7] A. Sadullaev, Pluripotential theory. Applications, Palmarium Academic Publishing, Germany, 2012