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

Journal of the Australian Mathematical Society

Walter R. Bloom¹ 

[1] Joseph F. Sussich

关键词: primary 41 A 65;    41 A 36;    secondary 43 A 22;    47 B 55;   

DOI  :  10.1017/S1446788700016475

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown