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Currently displaying 1 – 2 of 2

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Uniform approximation of harmonic functions

G. F. Vincent-Smith — 1969

Annales de l'institut Fourier

Let $ω$ be an open relatively compact weakly determining subset of a locally compact harmonic space in the axiomatic of Boboc-Constantinescu-Cornea. If $f$ is continuous on $\overline{ω}$ and harmonic in $ω$ the $f$ may be uniformly approximated on $\overline{ω}$ to within $ϵ$ by a function harmonic in an open set containing $\overline{ω}$ . The proof uses an extension of the Weierstrass-Stone theorem to geometric simplexes.

A Weierstrass-Stone theorem for Choquet simplexes

David Alan Edwards; G. F. Vincent-Smith — 1968

Annales de l'institut Fourier

Soit $X \neq \emptyset$ un convexe compact d’un espace localement convexe séparé, soit $A (X)$ l’espace de fonctions réelles affines continues sur $X$ , et soit $L$ un sous-espace de $A (X)$ linéaire qui contient les fonctions constantes. Parmi les faces fermées de $X$ sur lesquelles les fonctions de $L$ sont toutes constantes on appelle les faces maximales $L$ -faces. Nos théorèmes principaux donnent quelques conditions sous lesquelles $L$ contient exactement ces fonctions qui sont constantes sur chaque $L$ -face. En particulier, $L$ est dense...

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