Geodesic
Removable singularities of separately harmonic functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 369-375

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Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function $u(x,y)$ in $D\setminus S$ to the domain $D$, when $D\subset\mathbb{R}^n(x)\times\mathbb{R}^m(y)$, $n,m>1$ and $S$ is a closed subset of the domain $D$ with nowhere dense projections $S_1=\{x\in\mathbb{R}^n:(x,y)\in S\}$ and $S_2=\{y\in\mathbb{R}^m:(x,y)\in S\}$.
Keywords: separately harmonic function, $\mathcal P$-measure.
Mots-clés : pseudoconvex domain, Poisson integral 
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     title = {Removable singularities of separately harmonic functions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a9/}
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Sevdiyor A. Imomkulov; Sultanbay M. Abdikadirov. Removable singularities of separately harmonic functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 369-375. http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a9/