Journal article
Positive linear operators and the approximation of continuous functions on locally compact abelian groups
Journal of the Australian Mathematical Society (Series A), Vol.30(2), pp.180-186
1980
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.
Details
- Title
- Positive linear operators and the approximation of continuous functions on locally compact abelian groups
- Authors/Creators
- W.R. Bloom (Author/Creator)J.F. Sussich (Author/Creator)
- Publication Details
- Journal of the Australian Mathematical Society (Series A), Vol.30(2), pp.180-186
- Publisher
- Cambridge University Press
- Identifiers
- 991005542452107891
- Copyright
- © 1980 Australian Mathematical Society
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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