Article contents
Positive linear operators and the approximation of continuous functions on locally compact abelian groups
Published online by Cambridge University Press: 09 April 2009
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→rTnf = f uniformly for f = 1, cos and sin. then limn→rTnf = f uniformly for all f∈C. 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.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 180 - 186
- Copyright
- Copyright © Australian Mathematical Society 1980
References
- 3
- Cited by