On approximation of functions by singular integrals in the Hausdorff metric
Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 229-246
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Necessary and sufficient conditions are found for convergence in the Hausdorff metric of a sequence of integral operators on an arbitrary bounded measurable function. The criterion obtained is used to investigate summation of trigonometric Fourier series by the Abel–Poisson, Vallée-Poussin, Bernstein–Rogosinski, and Cesàro methods. Bibliography: 7 titles.
@article{SM_1989_63_1_a15,
author = {A. P. Petukhov},
title = {On approximation of functions by singular integrals in the {Hausdorff} metric},
journal = {Sbornik. Mathematics},
pages = {229--246},
year = {1989},
volume = {63},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1989_63_1_a15/}
}
A. P. Petukhov. On approximation of functions by singular integrals in the Hausdorff metric. Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 229-246. http://geodesic.mathdoc.fr/item/SM_1989_63_1_a15/
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