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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 2, Pages 125–144 (Mi izv636)  

This article is cited in 5 scientific papers (total in 5 papers)

On holomorphic continuation of functions defined on a pencil of boundary complex lines

S. A. Imomkulov

Al-Kharezmi Urgench State University, Khorezm, Uzbekistan

Abstract: We study domains of holomorphy of functions having thin singularities along a fixed direction. We prove a boundary analogue of Hartogs' theorem on the holomorphic continuation of functions of several variables that admit holomorphic continuation in one variable.

DOI: https://doi.org/10.4213/im636

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English version:
Izvestiya: Mathematics, 2005, 69:2, 345–363

Bibliographic databases:

UDC: 517.55
MSC: 32D99, 32A20
Received: 28.01.2004

Citation: S. A. Imomkulov, “On holomorphic continuation of functions defined on a pencil of boundary complex lines”, Izv. RAN. Ser. Mat., 69:2 (2005), 125–144; Izv. Math., 69:2 (2005), 345–363

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. A. S. Sadullaev, S. A. Imomkulov, “Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections”, Proc. Steklov Inst. Math., 253 (2006), 144–159  mathnet  crossref  mathscinet
    2. A. A. Atamuratov, “On Meromorphic Continuation in a Fixed Direction”, Math. Notes, 86:3 (2009), 301–305  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Viêt-Anh Nguyên, Pflug P., “Boundary cross theorem in dimension 1 with singularities”, Indiana Univ. Math. J., 58:1 (2009), 393–414  crossref  mathscinet  zmath  isi  scopus
    4. Viet-Anh Nguyen, “Recent Developments in the Theory of Separately Holomorphic Mappings”, Colloquium Mathematicum, 117:2 (2009), 175–206  crossref  mathscinet  zmath  isi  scopus
    5. A. Sadullaev, Z. Ibragimov, “The class $R$ and finely analytic functions”, Sb. Math., 209:8 (2018), 1234–1247  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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