Steklov Institute of Mathematics (RAS)
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Keywords: VC-dimension, Kolmogorov widths, lower bounds in approximation theory.
Publications (recent):
2024
→ I. V. Limonova, Yu. V. Malykhin, V. N. Temlyakov, "One-sided discretization inequalities and recovery from samples", Uspekhi Mat. Nauk, 79:3 (477) (2024), 149–180, DOI.
→ Yu. V. Malykhin, "Widths and rigidity", Mat. Sb., 215:4 (2024), 117–148, DOI.
2023
→ Yu. V. Malykhin, E. V. Shchepin, "Search of fractal space-filling curves with minimal dilation", Discrete Comput. Geom., 70 (2023), 189–213, DOI, arXiv.
2022
→ Yu. V. Malykhin, "A complete description of the relative widths of Sobolev classes in the uniform metric", Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022), 137–142, DOI.
→ Yu. V. Malykhin, E. V. Shchepin, "Search of fractal space-filling curves with minimal dilation", Discrete Comput. Geom., 2022, 1–35, DOI, arXiv.
→ Yu. V. Malykhin, K. S. Ryutin, T. I. Zaitseva, "Recovery of regular ridge functions on the ball", Constr Approx (2022), DOI, arXiv.
→ Yu. V. Malykhin, "Matrix and tensor rigidity and \(L_p\)-approximation", J. Complexity, 2022, 1–13, DOI, arXiv.
2021
→ Yu. V. Malykhin, "Kolmogorov Widths of the Besov Classes \(B_{1,1}^\theta\) and Products of Octahedra", Proc. Steklov Inst. Math., 312 (2021), 215–225, DOI, arXiv.
→ T. I. Zaitseva, Yu. V. Malykhin, K. S. Ryutin, "On Recovery of Regular Ridge Functions", Math. Notes, 109:2 (2021), 307–311, DOI.
2020
→ Yu. V. Malykhin, E. V. Shchepin, "Minimal self-similar Peano curve of genus \(5×5\)", Dokl. RAN. Math. Inf. Proc. upr., 491:1 (2020), 68–72, DOI.
2018
→ B. S. Kashin, Yu. V. Malykhin, K. S. Ryutin, "Kolmogorov width and approximate rank", Proc. Steklov Inst. Math., 303 (2018), 140–153, DOI.
2017
→ Yu. V. Malykhin, K. S. Ryutin, "The Product of Octahedra is Badly Approximated in the \(\ell_{2,1}\)-Metric", Math. Notes, 101:1 (2017), 94–99, DOI, arXiv.
→ Yu. V. Malykhin, E. V. Shchepin, "Chain development of metric compacts", Topology Appl., 221 (2017), 624–629 , DOI, arXiv.
→ E. S. Belkina, Y. V. Malykhin, "Fourier coefficients of continuous functions with respect to localized Haar system", Issues Anal., 6(24):1 (2017), 11–18, DOI.