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Best quadrature formulae and methods for reconstructing functions defined by kernels not extending oscillation. (Russian) Zbl 0613.41026
It is proved that the rectangle formula is the optimal quadrature formula on the class of functions defined by the kernels not extending oscillation, e.g. Poisson’s kernel, de la Vallée Poussin’s kernel, \(\sum^{\infty}_{k=-\infty}(1/ch 2\pi kh)e^{2\pi ikx}\) and others. Moreover, the solution of the Favard problem is given and a construction of best methods for reconstructing functions from the classes generated by the kernels not extending oscillation is presented.
Reviewer: J.Albrycht

MSC:
41A55 Approximate quadratures
41A50 Best approximation, Chebyshev systems
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