A. M. Kytmanov, S. G. Myslivets, “On Families of Complex Lines Sufficient for Holomorphic Extension”, Mat. Zametki, 83:4 (2008), 545–551; Math. Notes, 83:4 (2008), 500

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Matematicheskie Zametki, 2008, Volume 83, Issue 4, Pages 545–551
DOI: https://doi.org/10.4213/mzm3770 (Mi mzm3770)

This article is cited in 26 scientific papers (total in 26 papers)

On Families of Complex Lines Sufficient for Holomorphic Extension

A. M. Kytmanov, S. G. Myslivets

Krasnoyarsk State University

Full-text PDF (463 kB) Citations (26)

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DOI: https://doi.org/10.4213/mzm3770

Abstract: It is shown that the set

$\mathfrak L_\Gamma$ of all complex lines passing through a germ of a generating manifold

$\Gamma$ is sufficient for any continuous function

$f$ defined on the boundary of a bounded domain

$D\subset\mathbb C^n$ with connected smooth boundary and having the holomorphic one-dimensional extension property along all lines from

$\mathfrak L_\Gamma$ to admit a holomorphic extension to

$D$ as a function of many complex variables.

Keywords: holomorphic extension property, family of complex lines, Hartogs' theorem, Bochner–Martinelli integral, Sard's theorem, Cauchy–Riemann condition.

Received: 03.07.2006
Revised: 26.03.2007

English version:
Mathematical Notes, 2008, Volume 83, Issue 4, Pages 500–505
DOI: https://doi.org/10.1134/S0001434608030231

Bibliographic databases:

UDC: 517.55

Language: Russian

Citation: A. M. Kytmanov, S. G. Myslivets, “On Families of Complex Lines Sufficient for Holomorphic Extension”, Mat. Zametki, 83:4 (2008), 545–551; Math. Notes, 83:4 (2008), 500–505

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Linking options:

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This publication is cited in the following 26 articles:

Bakhodir A. Shoimkhulov, Baymurat J. Kutlimuratov, “Some classes of sets sufficient for holomorphic continuation of integrable functions”, Zhurn. SFU. Ser. Matem. i fiz., 17:4 (2024), 506–512
G. Khudayberganov, “Multidimensional Boundary Morera Theorems in Matrix Domains”, J Math Sci, 284:2 (2024), 216
A. M. Kytmanov, S. G. Myslivets, “O nekotorykh mnozhestvakh, dostatochnykh dlya golomorfnogo prodolzheniya funktsii s obobschennym granichnym svoistvom Morera”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:3 (2023), 483–496
Simona G. Myslivets, “On the multidimensional boundary analogue of the Morera theorem”, Zhurn. SFU. Ser. Matem. i fiz., 15:1 (2022), 29–45
A. M. Kytmanov, S. G. Myslivets, “On functions with the boundary Morera property in domains with piecewise-smooth boundary”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:1 (2021), 50–58
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 Math. J., 12:3 (2020), 44–49
Tryfonos C., Vidras A., “Boundary Behavior of Functions Representable By Weighted Koppelman Type Integral and Related Hartogs Phenomenon”, Comput. Methods Funct. Theory, 20:1 (2020), 5–38
Simona G. Myslivets, “Functions with the one-dimensional holomorphic extension property”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 439–443
Kytmanov A.M., Myslivets S.G., “On Functions With One-Dimensional Holomorphic Extension Property in Circular Domains”, Math. Nachr., 292:6 (2019), 1321–1332
Alexander M. Kytmanov, Simona G. Myslivets, “Multidimensional boundary analog of the Hartogs theorem in circular domains”, Zhurn. SFU. Ser. Matem. i fiz., 11:1 (2018), 79–90
Bairambay Otemuratov, Springer Proceedings in Mathematics & Statistics, 264, Algebra, Complex Analysis, and Pluripotential Theory, 2018, 109
A. M. Kytmanov, S. G. Myslivets, “Holomorphic extension of functions along finite families of complex straight lines in an $n$ -circular domain”, Siberian Math. J., 57:4 (2016), 618–631
Kytmanov A.M., Myslivets S.G., “An Analog of the Hartogs Theorem in a Ball of $\mathbb C^n$ ”, Math. Nachr., 288:2-3 (2015), 224–234
Alexander M. Kytmanov, Simona G. Myslivets, “Holomorphic extension of continuous functions along finite families of complex lines in a ball”, Zhurn. SFU. Ser. Matem. i fiz., 8:3 (2015), 291–302
Alexander M. Kytmanov, Simona G. Myslivets, Multidimensional Integral Representations, 2015, 119
V. I. Kuzovatov, A. M. Kytmanov, “On a boundary analog of the Forelli theorem”, Siberian Math. J., 54:5 (2013), 841–856
Kytmanov A.M., Myslivets S.G., “On the Families of Complex Lines Sufficient for Holomorphic Continuation of Functions Defined on a Domain Boundary”, Complex Analysis and Dynamical Systems V, Contemporary Mathematics, 591, eds. Agranovsky M., BenArtzi M., Galloway G., Karp L., Mazya V., Reich S., Shoikhet D., Weinstein G., Zal, Amer Mathematical Soc, 2013, 159–170
Bairambai P. Otemuratov, “Nekotorye mnozhestva kompleksnykh pryamykh minimalnoi razmernosti, dostatochnye dlya golomorfnogo prodolzheniya integriruemykh funktsii”, Zhurn. SFU. Ser. Matem. i fiz., 5:1 (2012), 97–105
Aleksandr M. Kytmanov, Simona G. Myslivets, “O semeistvakh kompleksnykh pryamykh, dostatochnykh dlya golomorfnogo prodolzheniya funktsii, zadannykh na granitse oblasti”, Zhurn. SFU. Ser. Matem. i fiz., 5:2 (2012), 213–222
V. I. Kuzovatov, “O nekotorykh semeistvakh kompleksnykh pryamykh, dostatochnykh dlya golomorfnogo prodolzheniya funktsii”, Ufimsk. matem. zhurn., 4:1 (2012), 107–121

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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