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Mat. Zametki, 2008, Volume 83, Issue 4, Pages 545–551 (Mi mz3770)  

This article is cited in 16 scientific papers (total in 16 papers)

On Families of Complex Lines Sufficient for Holomorphic Extension

A. M. Kytmanov, S. G. Myslivets

Krasnoyarsk State University

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

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

Full text: PDF file (463 kB)
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English version:
Mathematical Notes, 2008, 83:4, 500–505

Bibliographic databases:

UDC: 517.55
Received: 03.07.2006
Revised: 26.03.2007

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alexander M. Kytmanov, “Some application of the Bochner–Martinelli integral”, Zhurn. SFU. Ser. Matem. i fiz., 4:1 (2011), 32–42  mathnet  elib
    2. A. M. Kytmanov, S. G. Myslivets, “Some families of complex lines sufficient for holomorphic continuation of functions”, Russian Math. (Iz. VUZ), 55:4 (2011), 60–66  mathnet  crossref  mathscinet
    3. A. M. Kytmanov, S. G. Myslivets, V. I. Kuzovatov, “Minimal dimension families of complex lines sufficient for holomorphic extension of functions”, Siberian Math. J., 52:2 (2011), 256–266  mathnet  crossref  mathscinet  isi
    4. Agranovsky M.L., “Analog of a theorem of Forelli for boundary values of holomorphic functions on the unit ball of $\mathbb C^n$”, J. Anal. Math., 113 (2011), 293–304  crossref  mathscinet  zmath  isi  elib  scopus
    5. 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  mathnet
    6. 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  mathnet
    7. V. I. Kuzovatov, “O nekotorykh semeistvakh kompleksnykh pryamykh, dostatochnykh dlya golomorfnogo prodolzheniya funktsii”, Ufimsk. matem. zhurn., 4:1 (2012), 107–121  mathnet
    8. Aleksandr M. Kytmanov, Simona G. Myslivets, “Golomorfnoe prodolzhenie funktsii vdol konechnykh semeistv kompleksnykh pryamykh v share”, Zhurn. SFU. Ser. Matem. i fiz., 5:4 (2012), 547–557  mathnet
    9. Globevnik J., “Meromorphic extensions from small families of circles and holomorphic extensions from spheres”, Trans. Am. Math. Soc., 364:11 (2012), 5857–5880  crossref  mathscinet  zmath  isi  elib  scopus
    10. V. I. Kuzovatov, A. M. Kytmanov, “On a boundary analog of the Forelli theorem”, Siberian Math. J., 54:5 (2013), 841–856  mathnet  crossref  mathscinet  isi
    11. 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  crossref  mathscinet  zmath  isi
    12. 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  crossref  mathscinet  zmath  isi  scopus
    13. 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  mathnet  crossref
    14. 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  mathnet  crossref  crossref  isi  elib  elib
    15. 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  mathnet  crossref
    16. Simona G. Myslivets, “Functions with the one-dimensional holomorphic extension property”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 439–443  mathnet  crossref
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