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Sevdiyor Imomkulov

Publications and source records attributed to Sevdiyor Imomkulov.

3 recordsLinked to original sources
arXiv2009

An extension of harmonic functions along fixed direction

Let a function $u(x,y)$ be harmonic in the domain $$ D\times V_r=D\times \{y\in \mathbb{R}^m: |y|<r\}\subset \mathbb{R}^n\times \mathbb{R}^m $$ and for each fixed point $x^0$ from some a set $E\subset D$, %which is not embedded in countable association of $N$-sets of $ Lh_0(D)$, the function $u(x^0,y)$, as a function of variable $y$, can be extended to a harmonic function on the whole $\mathbb{R}^m$. Then $u(x,y)$ harmonically extends to the domain $D\times \mathbb{R}^m$ as a function of variables $x$ and $y$.

math.CV↗
arXiv2009

Pluripolarity of graphs of quasianalytic functions in the sense of Gonchar

We study functions defined on a closed segment of the real line that belong to the class of Gonchar. We show that the graphs of such functions are pluripolar. We also discuss the generalizations of our result to functions defined on a compact subset of C^n that belong to the class of Gonchar.

math.CV↗