Geodesic
Some classes of sets sufficient for holomorphic continuation of integrable functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 506-512.

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In the present work we consider integrable functions defined on a boundary of a bounded domain $D$ in ${{\mathbb{C}}^{n}}$, $n>1$, and possessing a generalized Morera boundary property. We show that such functions possess a holomorphic continuation into the domain $D$ for some sufficient sets $\Gamma$ of complex lines.
Keywords: holomorphic continuation, Morera boundary condition, Bochner–Martinelli kernel. 
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Bakhodir A. Shoimkhulov; Baymurat J. Kutlimuratov. Some classes of sets sufficient for holomorphic continuation of integrable functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 506-512. http://geodesic.mathdoc.fr/item/JSFU_2024_17_4_a8/

[1] E.A.Grinberg, “A boundary analogue of Morera's theorem in the unit ball of $C^n$”, Proceedings of the American Society, 102:1 (1988), 114–116 | MR | Zbl

[2] M.L.Agranovskii, R.E.Valskii, “Maximality of invariant algebras of functions”, Siberian Mathematical Journ, 12:1 (1971), 1–7 | DOI | MR

[3] J.Globevnik, E.L.Stout, “Boundary Morera theorems for holomorphic functions of several complex variables”, Duke Mathematical Journal, 64:3 (1991), 571–615 | DOI | MR | Zbl

[4] J.Globevnik, “A boundary Morera theorem”, Jounal of Geometric Analysis, 3:3 (1993), 269–277 | DOI | MR | Zbl

[5] D.Govekar-Leban, “Local boundary Morera theorems”, Mathematische Zeitschrift, 233 (2000), 265–286 | DOI | MR | Zbl

[6] S.G.Myslivets, “One boundary version of Morera's theorem”, Siberian Mathematical Journal, 42:5 (2001), 952–960 | DOI | MR | Zbl

[7] A.M.Kytmanov, S.G.Myslivets, “On families of complex lines sufficient for holomorphic extension”, Mathematical Notes, 83:4 (2008), 500–505 | DOI | MR | Zbl

[8] A.M.Kytmanov, S.G.Myslivets, “Some families of complex lines sufficient for holomorphic extension of functions”, Russian Mathematic (Iz. VUZ), 55:4 (2011) | DOI | MR | Zbl

[9] A.M.Kytmanov, S.G.Myslivets, “On family of complex straight lines sufficient for existence of holomorphic continuation of continuous functions on boundary of domain”, Ufa Mathematical Journal, 12:3 (2020), 45–50 | DOI | MR | Zbl

[10] A.M.Kytmanov, S.G.Myslivets, “On some sets sufficient for holomorphic continuation of functions with generalized boundary Morera property”, Udmurd University Journal, 33:3 (2023), 483-496 (in Russian) | MR | Zbl

[11] B.P.Otemuratov, “On functions with one-dimensional holomorphic extension property”, Vestnik KrasGU, 2006, no. 9, 95–100

[12] B.T.Kurbanov, “Morera's Boundary Theorem in Siegel Domain of the First Kind”, J. Sib. Fed. Univ. Math. Phys., 15:2 (2022), 255–262 | DOI | MR | Zbl

[13] A.M.Kytmanov, S.G.Myslivets, Multidimensional Integral Representations, Problems of Analytic Continuation, Springer Verlag, Basel–Boston, 2015 | MR | Zbl

[14] K.Ghudayberganov, A.M.Kytmanov, B.A.Shaymkulov, Analysis in matrix domains, Siberian Federal University, Institute of Mathematics and Fundamental Informatics, SFU, Krasnoyarsk, 2017 (in Russian)