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S. N. Kudryavtsev

Publications and source records attributed to S. N. Kudryavtsev.

11 recordsLinked to original sources
arXiv2026

Approximation of partial differential operators on Nikolskii-Besov functions classes of mixed smoothness in domains of a certain kind

The article examines Nikolskii and Besov spaces with norms defined using "$L_p$-averaged" mixed moduli of continuity for functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The work provides upper and lower estimates for a quantity of the best accuracy of approximation in the S.B.Stechkin problem for partial differential operators on a classes of such functions defined in domains of a certain kind. These estimates are not weaker, but in some cases even stronger than those derived by the author in the problem under consideration for the aforementioned classes of functions on cube $ I^d. $ It also significantly broadens the class of Nikolskii and Besov spaces of mixed smoothness for which mentioned estimates in the problem under consideration have been derived.

math.FA↗
arXiv2026

Extending functions from Nikolskii-Besov spaces of mixed smoothness beyond domains of certain kind

The article examines Nikolskii and Besov spaces with norms defined using $L_p$-averaged mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The author builds continuous linear mappings of such spaces of functions defined in domains of certain type to ordinary Nikolskii and Besov spaces of mixed smoothness in $ \mathbb R^d, $ that are function extension operators, thus incurring coincidence of both kinds of spaces in the said domains. It also significantly broadens the class of Nikolskii and Besov spaces of mixed smoothness for which the theorems of those kind of extension have been derived. Under certain conditions, operators of partial differentiation from the aforementioned function spaces of mixed smoothness to Lebesgue spaces have been established to be continuous.

math.CA↗
arXiv2026

Reconstruction derivatives from values of functions belonging to Nikolskii-Besov classes of mixed smoothness in domains of a certain kind

The article examines Nikolskii and Besov spaces with norms defined using "$L_p$-averaged" mixed moduli of continuity for functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The work provides upper and lower estimates of the best accuracy of reconstruction derivatives from function values at a given number of points for such classes of functions in bounded domains of a certain kind. These estimates are not weaker, but in some cases even stronger than those derived by the author in the problem under consideration for the aforementioned classes of functions on cube $ I^d. $ It also significantly broadens the class of Nikolskii and Besov spaces of mixed smoothness for which mentioned estimates in the problem under consideration have been derived.

math.CA↗
arXiv2025

Bernstein widths of nonisotropic Nikolskii-Besov classes

The article examines nonisotropic Nikolskii and Besov spaces with norms defined using $L_p$-averaged moduli of continuity of functions of appropriate orders along the coordinate directions, instead of moduli of continuity of known orders for derivative functions along the same directions. For the unit balls of such spaces of functions defined in domains of certain type, weak asymptotics of Bernstein $n$-widths behavior in $L_q$-spaces has been obtained.

math.CA↗
arXiv2019

Extending functions from Nikolskii-Besov spaces of mixed smoothness beyond a cube

The article examines Nikolskii and Besov spaces with norms defined using "$L_p$-averaged" mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The author builds continuous linear mappings of such spaces of functions defined on cube $ I^d, $ to ordinary Nikolskii and Besov spaces of mixed smoothness in $ \mathbb R^d, $ that are function extension operators, thus incurring coincidence of both kinds of spaces on the cube $ I^d. $

math.CA↗
arXiv2019

Extending functions from isotropic Nikolskii-Besov spaces and their approximating with derivatives

The article examines isotropic Nikolskii and Besov spaces with norms defined using $L_p$-averaged modulus of continuity of functions of appropriate order, instead of modulus of continuity of known order for fixed-order partial derivative functions. The author builds continuous linear mappings of such spaces of functions defined in domains of $(1,\ldots,1)$-type (in a broad sense) to ordinary isotropic Nikolskii and Besov spaces in $ \mathbb R^d $ that are function extension operators, thus incurring coincidence of both kinds of spaces in the said domains. It is established that every bounded domain in $ \mathbb R^d $ with a Lipschitzian boundary is a $(1,\ldots,1)$-type domain (in a broad sense). The article also provides weak asymptotics of approximation characteristics related to the problem of reconstruction of functions with their derivatives from function values at a given number of points, the S.B.Stechkin's problem for differential operator, and the problem of width asymptotics for isotropic Nikolskii-Besov classes in those domains.

math.CA↗
arXiv2018

Extending functions from nonisotropic Nikolskii-Besov spaces and approximating their derivatives (with supplement)

The article examines nonisotropic Nikolskii and Besov spaces with norms defined using $L_p$-averaged moduli of continuity of functions of appropriate orders along the coordinate directions, instead of moduli of continuity of known orders for derivative functions along the same directions. The author builds continuous linear mappings of such spaces of functions defined in domains of certain type to ordinary nonisotropic Nikolskii and Besov spaces in $\mathbb{R}^d $ that are function extension operators, thus incurring coincidence of both kinds of spaces in the said domains. The article also provides weak asymptotics of approximation characteristics related to the problem of derivative reconstruction from function values at a given number of points, the S.B.Stechkin's problem for differential operator, and the problem of width asymptotics for nonisotropic Nikolskii-Besov classes in those domains. The supplement provides a broad-sense definition of $α$-type domain. It is demonstrated that all of the earlier statements established by the author with respect to the tasks of function extension, derivative reconstruction from function values, differential operator approximation with bounded operators, and width asymptotics for nonisotropic Nikolskii-Besov function classes defined in $α$-type domains (in a narrow sense), remain valid in the same formulation even for an $α$-type domain as construed in a broad sense.

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arXiv2014

Upper estimate of the best accuracy of derivative reconstruction based on the values of functions of Besov classes with mixed smoothness

The work provides an upper estimate of the best accuracy for the problem of reconstructing derivatives based on function values at a given number of points for the functions of Besov classes meeting the mixed Hoelder conditions. In some cases this estimate appears to be stronger than the earlier respective estimate obtained by the author in the problem being considered.

math.CA↗
arXiv2011

A Littlewood-Paley type theorem on orthoprojectors onto mutually orthogonal subspaces of piecewise polynomial functions and its corollary

The article proves an assertion analogous to the Littlewood-Paley theorem for the orthoprojectors onto mutually orthogonal subspaces of piecewise polynomial functions on the cube $ I^d. $ This assertion provides an upper estimate for the norms of the functions in $ L_p(I^d) $ via corresponding norms of projections onto subspaces of piecewise polynomial multivariable functions. These relationships are used to obtain upper estimates of the Kolmogorov widths of Besov classes of non-periodic functions meeting the mixed Hoelder conditions.

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