Geodesic
Kolmogorov widths of an~intersection of a~finite family of Sobolev classes
Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 18-42.

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

Order estimates for the Kolmogorov widths of an intersection of Sobolev classes on a $d$-dimensional John domain and on the 1-dimensional torus are obtained. In particular, one Galeev's result is generalized.
Keywords: Kolmogorov width, intersection of Sobolev classes. 
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A. A. Vasil'eva. Kolmogorov widths of an~intersection of a~finite family of Sobolev classes. Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 18-42. http://geodesic.mathdoc.fr/item/IM2_2024_88_1_a1/

[1] È. M. Galeev, “The Kolmogorov diameter of the intersection of classes of periodic functions and of finite-dimensional sets”, Math. Notes, 29:5 (1981), 382–388 | DOI

[2] È. M. Galeev, “Kolmogorov widths of classes of periodic functions of one and several variables”, Math. USSR-Izv., 36:2 (1991), 435–448 | DOI

[3] E. M. Galeev, “Kolmogorov and linear diameters of functional classes and finite dimensional sets”, Vladikavkaz. Mat. Zh., 13:2 (2011), 3–14 (Russian) | MR | Zbl

[4] A. A. Vasil'eva, “Kolmogorov widths of intersections of finite-dimensional balls”, J. Complexity, 72 (2022), 101649 | DOI | MR | Zbl

[5] A. A. Vasil'eva, “Kolmogorov widths of weighted Sobolev classes on a multi-dimensional domain with conditions on the derivatives of order $r$ and zero”, J. Approx. Theory, 269 (2021), 105602 | DOI | MR | Zbl

[6] A. A. Vasil'eva, “Bounds for the Kolmogorov widths of the Sobolev weighted classes with conditions on the zero and highest derivatives”, Russ. J. Math. Phys., 29:2 (2022), 249–279 | DOI | MR | Zbl

[7] V. M. Tikhomirov, Some questions in approximation theory, Izd-vo Mosk. Univ., Moscow, 1976 (Russian) | MR

[8] V. M. Tikhomirov, “Approximation theory”, Analysis, v. II, Encyclopaedia Math. Sci., 14, Convex analysis and approximation theory, Springer-Verlag, Berlin, 1990, 93–243 | DOI | MR | Zbl

[9] A. Pinkus, $n$-widths in approximation theory, Ergeb. Math. Grenzgeb. (3), 7, Springer-Verlag, Berlin, 1985 | DOI | MR | Zbl

[10] S. L. Sobolev, Applications of functional analysis in mathematical physics, Transl. Math. Monogr., 7, Amer. Math. Soc., Providence, RI, 1963 | MR | Zbl

[11] Yu. G. Reshetnyak, “Integral representations of differentiable functions in domains with nonsmooth boundary”, Siberian Math. J., 21:6 (1980), 833–839 | DOI

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

[13] È. M. Galeev, “Approximation by Fourier sums of classes of functions with several bounded derivatives”, Math. Notes, 23:2 (1978), 109–117 | DOI

[14] A. Pietsch, “$s$-numbers of operators in Banach space”, Studia Math., 51 (1974), 201–223 | DOI | MR | Zbl

[15] M. I. Stesin, “Aleksandrov diameters of finite-dimensional sets and classes of smooth functions”, Soviet Math. Dokl., 16 (1975), 252–256 | Zbl

[16] B. S. Kašin, “Diameters of some finite-dimensional sets and classes of smooth functions”, Math. USSR-Izv., 11:2 (1977), 317–333 | DOI

[17] E. D. Gluskin, “On some finite-dimensional problems of the theory of diameters”, Vestn. Leningr. Univ., 13 (1981), 5–10 (Russian) | Zbl

[18] E. D. Gluskin, “Norms of random matrices and widths of finite-dimensional sets”, Math. USSR-Sb., 48:1 (1984), 173–182 | DOI

[19] A. Yu. Garnaev and E. D. Gluskin, “On widths of the Euclidean ball”, Soviet Math. Dokl., 30 (1984), 200–204

[20] O. V. Besov, “Kolmogorov widths of Sobolev classes on an irregular domain”, Proc. Steklov Inst. Math., 280 (2013), 34–45 | DOI

[21] A. A. Vasil'eva, “Widths of weighted Sobolev classes on a John domain”, Proc. Steklov Inst. Math., 280 (2013), 91–119 | DOI

[22] S. M. Nikol'skiĭ, Approximation of functions of several variables and imbedding theorems, Grundlehren Math. Wiss., 205, Springer-Verlag, New York–Heidelberg, 1975 | DOI | MR | Zbl

[23] O. V. Besov, V. P. Il'in, and S. M. Nikol'skiĭ, Integral representations of functions and imbedding theorems, v. I, II, Scripta Series in Mathematics, V. H. Winston Sons, Washington, DC; Halsted Press [John Wiley Sons], New York–Toronto, ON–London, 1978, 1979 | MR | MR | Zbl

[24] M. Bricchi, “Existence and properties of $h$-sets”, Georgian Math. J., 9:1 (2002), 13–32 | DOI | MR | Zbl