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An extension of a theorem of P. P. Korovkin to singular integrals with not necessarily positive kernels

Authors
Journal
Indagationes Mathematicae (Proceedings)
1385-7258
Publisher
Elsevier
Publication Date
Volume
75
Issue
3
Identifiers
DOI: 10.1016/1385-7258(72)90060-1
Disciplines
  • Mathematics

Abstract

Abstract Concerning the approximation of periodic functions by means of singular convolution integrals having positive trigonometric kernels, an equivalence theorem of P. P. Korovkin on convergence factors, i.e., on the Fourier coefficients of the kernel, is of great importance. A simple inversion formula between convergence factors and trigonometric moments of a general kernel immediately delivers an extension of this theorem to a class of singular integrals with not necessarily positive kernels as well as a simplified proof of the original result. The new theorem is applied to three representative examples of oscillating kernels.

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