Geodesic
Constructive description of function classes on surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$
Problemy analiza, Tome 8 (2019) no. 3, pp. 16-23

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Functional classes on a curve in a plane (a partial case of a spatial curve) can be described by the approximation speed by functions that are harmonic in three-dimensional neighbourhoods of the curve. No constructive description of functional classes on rather general surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$ has been presented in literature so far. The main result of the paper is Theorem 1.
Keywords: constructive description, rational functions, harmonic functions, pseudoharmonic functions. 
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     author = {T. A. Alexeeva and N. A. Shirokov},
     title = {Constructive description  of function classes on surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$},
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     pages = {16--23},
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     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_3_a1/}
}
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T. A. Alexeeva; N. A. Shirokov. Constructive description  of function classes on surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$. Problemy analiza, Tome 8 (2019) no. 3, pp. 16-23. http://geodesic.mathdoc.fr/item/PA_2019_8_3_a1/