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

Autor:	Walter R. Bloom, Joseph F. Sussich
Rok vydání:	1980
Předmět:	Discrete mathematics Sequence Pure mathematics Riesz–Markov–Kakutani representation theorem Elementary abelian group General Medicine Locally compact space Locally compact group Abelian group Space (mathematics) Character group Mathematics
Zdroj:	Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics. 30:180-186
ISSN:	0263-6115
DOI:	10.1017/s1446788700016475
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::fb1baed3d580218f1417e9eed64e62e9 https://doi.org/10.1017/s1446788700016475 Zobrazit plný text záznamu