Kolmogorov widths of weighted Sobolev classes with “small” singularity sets
Eurasian mathematical journal, Tome 10 (2019) no. 1, pp. 89-92.

Voir la notice de l'article provenant de la source Math-Net.Ru

Sharp order estimates are stated for the Kolmogorov widths of weighted Sobolev classes on $h$-sets foe sertain limiting cases of the parameters.
@article{EMJ_2019_10_1_a7,
     author = {A. A. Vasil'eva},
     title = {Kolmogorov widths of weighted {Sobolev} classes with {\textquotedblleft}small{\textquotedblright} singularity sets},
     journal = {Eurasian mathematical journal},
     pages = {89--92},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2019_10_1_a7/}
}
TY  - JOUR
AU  - A. A. Vasil'eva
TI  - Kolmogorov widths of weighted Sobolev classes with “small” singularity sets
JO  - Eurasian mathematical journal
PY  - 2019
SP  - 89
EP  - 92
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2019_10_1_a7/
LA  - en
ID  - EMJ_2019_10_1_a7
ER  - 
%0 Journal Article
%A A. A. Vasil'eva
%T Kolmogorov widths of weighted Sobolev classes with “small” singularity sets
%J Eurasian mathematical journal
%D 2019
%P 89-92
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2019_10_1_a7/
%G en
%F EMJ_2019_10_1_a7
A. A. Vasil'eva. Kolmogorov widths of weighted Sobolev classes with “small” singularity sets. Eurasian mathematical journal, Tome 10 (2019) no. 1, pp. 89-92. http://geodesic.mathdoc.fr/item/EMJ_2019_10_1_a7/

[1] I.V. Boykov, “Approximation of some classes of functions by local splines”, Comput. Math. Math. Phys., 38:1 (1998), 21–29 | MR

[2] I.V. Boykov, Optimal approximation and Kolmogorov widths estimates for certain singular classes related to equations of mathematical physics, arXiv: 1303.0416v1

[3] M. Bricchi, “Existence and properties of h-sets”, Georgian Mathematical Journal, 9:1 (2002), 13–32 | MR | Zbl

[4] T. Mieth, “Entropy and approximation numbers of embeddings of weighted Sobolev spaces”, J. Appr. Theory, 192 (2015), 250–272 | DOI | MR | Zbl

[5] T. Mieth, “Entropy and approximation numbers of weighted Sobolev spaces via bracketing”, J. Funct. Anal., 270:11 (2016), 4322–4339 | DOI | MR | Zbl

[6] A. Pinkus, $n$-widths in approximation theory, Springer, Berlin, 1985 | MR | Zbl

[7] Yu.G. Reshetnyak, “Integral representations of differentiable functions in domains with a nonsmooth boundary”, Sibirsk. Mat. Zh., 21:6 (1980), 108–116 (in Russian) | MR | Zbl

[8] Yu.G. Reshetnyak, “A remark on integral representations of differentiable functions of several variables”, Sibirsk. Mat. Zh., 25:5 (1984), 198–200 (in Russian) | MR | Zbl

[9] V.M. Tikhomirov, “Theory of approximations”, Current problems in mathematics. Fundamental directions, Itogi Nauki i Tekhniki, 14, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., M., 1987, 103–260 ; Encycl. Math. Sci., 14 (1990), 93–243 | MR

[10] H. Triebel, Interpolation theory. Function spaces. Differential operators, Dtsch. Verl. Wiss., Berlin, 1978 ; Mir, M., 1980 | MR | Zbl

[11] H. Triebel, “Entropy and approximation numbers of limiting embeddings, an approach via Hardy inequalities and quadratic forms”, J. Approx. Theory, 164:1 (2012), 31–46 | DOI | MR | Zbl

[12] A.A. Vasil'eva, “Widths of function classes on sets with tree-like structure”, J. Appr. Theory, 192 (2015), 19–59 | DOI | MR | Zbl