This article is cited in 3 papers

On approximation of functions by singular integrals in the Hausdorff metric

A. P. Petukhov


Abstract: 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.

UDC: 517.5

MSC: Primary 45P05, 45E10, 42B20; Secondary 42A24, 40G05, 40G10

Received: 06.01.1987

 English version: Mathematics of the USSR-Sbornik, 1989, 63:1, 229–246

Bibliographic databases:

• 
•