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Positive linear operators and the approximation of continuous functions on locally compact abelian groups
Journal article   Peer reviewed

Positive linear operators and the approximation of continuous functions on locally compact abelian groups

W.R. Bloom and J.F. Sussich
Journal of the Australian Mathematical Society (Series A), Vol.30(2), pp.180-186
1980
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Abstract

In 1953 P. P. Korovkin proved that if (Tn) is a sequence of positive linear operators defined on the space C of continuous real 2π-periodic functions and limn→r Tnf = f uniformly for f = 1, cos and sin. then limn→r Tnf = f uniformly for all fxs2208C. We extend this result to spaces of continuous functions defined on a locally compact abelian group G, with the test family {1, cos, sin} replaced by a set of generators of the character group of G.

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