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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{PA_2019_8_3_a1,
     author = {T. A. Alexeeva and N. A. Shirokov},
     title = {Constructive description of function classes on surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$},
     journal = {Problemy analiza},
     pages = {16--23},
     year = {2019},
     volume = {8},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_3_a1/}
}
TY  - JOUR
AU  - T. A. Alexeeva
AU  - N. A. Shirokov
TI  - Constructive description of function classes on surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$
JO  - Problemy analiza
PY  - 2019
SP  - 16
EP  - 23
VL  - 8
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/PA_2019_8_3_a1/
LA  - en
ID  - PA_2019_8_3_a1
ER  - 
%0 Journal Article
%A T. A. Alexeeva
%A N. A. Shirokov
%T Constructive description of function classes on surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$
%J Problemy analiza
%D 2019
%P 16-23
%V 8
%N 3
%U http://geodesic.mathdoc.fr/item/PA_2019_8_3_a1/
%G en
%F PA_2019_8_3_a1
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/

[1] Alexeeva T. A., Shirokov N. A., “Constructive description of Hölder-like classes on an arc in $\mathbb{R}^3$ by means of harmonic functions”, Journal of Approximation Theory, 249 (2020) (to appear) | DOI | MR | Zbl

[2] Andrievskii V. V., “Approximation characterization of classes of functions on continua of the complex plane”, Math USSR-Sb., 53:1 (1986), 69–87 | DOI | MR

[3] Russian Acad. Sci. Izv. Math., 44:1 (1995), 193–206 | DOI | MR

[4] Dzyadyk V. K., Introduction to the Theory of Uniform Approximation of Functions by Polynomials, Nauka, M., 1977 | MR | Zbl

[5] Shirokov N. A., “Approximation entropy of continua”, Dokl. Akad. Nauk SSSR, 235:3 (1977), 546–549 (in Russian) | MR

[6] Stein E. M., Singular integrals and differentiability properties of functions, Mir, M., 1973 | MR | Zbl