Standard

The best approximation of Laplace operator by linear bounded operators in the space L p. / Koshelev, A. A.
In: Russian Mathematics, Vol. 55, No. 6, 01.06.2011, p. 53-63.

Research output: Contribution to journal › Article › peer-review

Harvard

Koshelev, AA 2011, 'The best approximation of Laplace operator by linear bounded operators in the space L p', Russian Mathematics, vol. 55, no. 6, pp. 53-63. https://doi.org/10.3103/S1066369X11060089

APA

Koshelev, A. A. (2011). The best approximation of Laplace operator by linear bounded operators in the space L p. Russian Mathematics, 55(6), 53-63. https://doi.org/10.3103/S1066369X11060089

Vancouver

Koshelev AA. The best approximation of Laplace operator by linear bounded operators in the space L p. Russian Mathematics. 2011 Jun 1;55(6):53-63. doi: 10.3103/S1066369X11060089

Author

Koshelev, A. A. / The best approximation of Laplace operator by linear bounded operators in the space L p. In: Russian Mathematics. 2011 ; Vol. 55, No. 6. pp. 53-63.

BibTeX

@article{272987bec64f44e7a43df1bb585a21b6,
title = "The best approximation of Laplace operator by linear bounded operators in the space L p",
abstract = "We obtain close two-sided estimates for the best approximation of Laplace operator by linear bounded operators on the class of functions for which the square of the Laplace operator belongs to the Lp-space. We estimate the best constant in the corresponding Kolmogorov inequality and the error of the optimal recovery of values of the Laplace operator on functions from this class defined with an error. In a particular case (p = 2) we solve all three problems exactly.",
author = "Koshelev, {A. A.}",
note = "This work was supported by the Russian Foundation for Basic Research (grant 08-01-00213).",
year = "2011",
month = jun,
day = "1",
doi = "10.3103/S1066369X11060089",
language = "English",
volume = "55",
pages = "53--63",
journal = "Russian Mathematics",
issn = "1066-369X",
publisher = "Pleiades Publishing",
number = "6",

}

RIS

TY - JOUR

T1 - The best approximation of Laplace operator by linear bounded operators in the space L p

AU - Koshelev, A. A.

N1 - This work was supported by the Russian Foundation for Basic Research (grant 08-01-00213).

PY - 2011/6/1

Y1 - 2011/6/1

N2 - We obtain close two-sided estimates for the best approximation of Laplace operator by linear bounded operators on the class of functions for which the square of the Laplace operator belongs to the Lp-space. We estimate the best constant in the corresponding Kolmogorov inequality and the error of the optimal recovery of values of the Laplace operator on functions from this class defined with an error. In a particular case (p = 2) we solve all three problems exactly.

AB - We obtain close two-sided estimates for the best approximation of Laplace operator by linear bounded operators on the class of functions for which the square of the Laplace operator belongs to the Lp-space. We estimate the best constant in the corresponding Kolmogorov inequality and the error of the optimal recovery of values of the Laplace operator on functions from this class defined with an error. In a particular case (p = 2) we solve all three problems exactly.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=80051608667

U2 - 10.3103/S1066369X11060089

DO - 10.3103/S1066369X11060089

M3 - Article

VL - 55

SP - 53

EP - 63

JO - Russian Mathematics

JF - Russian Mathematics

SN - 1066-369X

IS - 6

ER -

ID: 38005262