A note on approximation of continuous functions on normed spaces

Autor:	M. A. Mytrofanov, A. V. Ravsky
Rok vydání:	2020
Předmět:	Polynomial Pure mathematics Continuous function General Mathematics Banach space Minimax approximation algorithm Functional Analysis (math.FA) Separable space Mathematics - Functional Analysis FOS: Mathematics 46G20 46T20 Normed vector space Mathematics Analytic function
Zdroj:	Carpathian Mathematical Publications. 12:107-110
ISSN:	2313-0210 2075-9827
DOI:	10.15330/cmp.12.1.107-110
Popis:	Let $X$ be a real separable normed space $X$ admitting a separating polynomial. We prove that each continuous function from a subset $A$ of $X$ to a real Banach space can be uniformly approximated by restrictions to $A$ of functions which are analytic on open subsets of $X$. Also we prove that each continuous function to a complex Banach space from a complex separable normed space admitting a separating $*$-polynomial can be uniformly approximated by $*$-analytic functions. Comment: 4 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1405b171bafce4d59d84ee2ab611df7f https://doi.org/10.15330/cmp.12.1.107-110 Zobrazit plný text záznamu