Abstract
In this paper we obtain estimates of the orders of Kolmogorov widths of the Besov classes B p,θ r(Td of periodic functions of several variables with dominant mixed derivative (defined in the sense of Weyl) in the space Lq, r∈ ℝd, 1<p,q< ∞, 0 < θ ≤ ∝. The proposed approach to calculating widths can also be used for finding the widths of the Sobolev classes Wp rTd) (by embedding them in the Besov classes Bp,θ r(Td)) as well as for calculating some other widths (such as Alexandroff, linear, projective, and orthoprojective widths).
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Galeev, É.M. Widths of the Besov Classes B p,θ r(Td). Mathematical Notes 69, 605–613 (2001). https://doi.org/10.1023/A:1010245407486
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DOI: https://doi.org/10.1023/A:1010245407486