Geodesic
Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 158-174

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The paper is of survey character. We present and discuss recent results concerning the extension of functions that admit holomorphic or plurisubharmonic extension in a fixed direction. These results are closely related to Hartogs' fundamental theorem, which states that if a function $f(z)$, $z = (z_1,z_2,\dots ,z_n)$, is holomorphic in a domain $D\subset \mathbb C^n$ in each variable $z_j$, then it is holomorphic in $D$ in the $n$-variable sense. 
@article{TM_2006_253_a12,
     author = {A. S. Sadullaev and S. A. Imomkulov},
     title = {Extension of {Holomorphic} and {Pluriharmonic} {Functions} with {Thin} {Singularities} on {Parallel} {Sections}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {158--174},
     publisher = {mathdoc},
     volume = {253},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_253_a12/}
}
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A. S. Sadullaev; S. A. Imomkulov. Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 158-174. http://geodesic.mathdoc.fr/item/TM_2006_253_a12/