Geodesic
A Bernstein–Walsh Type Inequality and Applications
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 256-264

Voir la notice de l'article provenant de la source Cambridge University Press

A Bernstein–Walsh type inequality for ${{C}^{\infty }}$ functions of several variables is derived, which then is applied to obtain analogs and generalizations of the following classical theorems: (1) Bochnak– Siciak theorem: a ${{C}^{\infty }}$ function on ${{\mathbb{R}}^{n}}$ that is real analytic on every line is real analytic; (2) Zorn–Lelong theorem: if a double power series $F\left( x,y \right)$ converges on a set of lines of positive capacity then $F\left( x,y \right)$ is convergent; (3) Abhyankar–Moh–Sathaye theorem: the transfinite diameter of the convergence set of a divergent series is zero.
DOI : 10.4153/CMB-2006-026-9
Mots-clés : 32A05, 26E05, Bernstein-Walsh inequality, convergence sets, analytic functions, ultradifferentiable functions, formal power series 
Neelon, Tejinder. A Bernstein–Walsh Type Inequality and Applications. Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 256-264. doi: 10.4153/CMB-2006-026-9
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