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The degree of approximation by positive operators on compact connected abelian groups

1982
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Journal of the Australian Mathematical Society
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In 1953 P. P. Korovkin proved that if (T n ) is a sequence of positive linear operators defined on the space C of continuous real 2w-periodic functions and lim T n f -f uniformly f o r / = 1, cos and sin, then lim T n f = f uniformly for all / e C. Quantitative versions of this result have been given, where the rate of convergence is given in terms of that of the test functions 1, cos and sin, and the modulus of continuity of /. We extend this result by giving a quantitative version of

doi:10.1017/s1446788700018796
fatcat:m3aaa2d3djfr5fdo7t64utulxm