Journal article
The degree of approximation by positive operators on compact connected abelian groups
Journal of the Australian Mathematical Society (Series A), Vol.33(03)
1982
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 2 π-periodic functions and lim Tnf = f uniformly for f = 1, cos and sin, then lim Tnf = f uniformly for all f xs2208 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 f. We extend this result by giving a quantitative version of Korovkin's theorem for compact connected abelian groups.
Details
- Title
- The degree of approximation by positive operators on compact connected 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.33(03)
- Publisher
- Cambridge University Press
- Identifiers
- 991005541330507891
- Copyright
- © 1982 Australian Mathematical Society
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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- Citation topics
- 9 Mathematics
- 9.270 Functional Analysis
- 9.270.1909 Approximation Operators
- Web Of Science research areas
- Mathematics
- Statistics & Probability
- ESI research areas
- Mathematics