Geodesic
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},
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     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_1_a15/}
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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/