1. CMB 2011 (vol 54 pp. 230)
 Clouâtre, Raphaël

Universal Power Series in $\mathbb{C}^N$
We establish the existence of power series in $\mathbb{C}^N$ with the property
that the subsequences of the sequence of partial sums uniformly
approach any holomorphic function on any well chosen compact subset
outside the set of convergence of the series. We also show that, in a
certain sense, most series enjoy this property.
Categories:32A05, 32E30 

2. CMB 2006 (vol 49 pp. 256)
 Neelon, Tejinder

A BernsteinWalsh Type Inequality and Applications
A BernsteinWalsh 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) BochnakSiciak
theorem: a $C^{\infty }$\ function on $\mathbb{R}^{n}$ that is real
analytic on every line is real analytic; (2) ZornLelong theorem: if a
double power series $F(x,y)$\ converges on a set of lines of positive
capacity then $F(x,y)$\ is convergent; (3) AbhyankarMohSathaye theorem:
the transfinite diameter of the convergence set of a divergent series is
zero.
Keywords:BernsteinWalsh inequality, convergence sets, analytic functions, ultradifferentiable functions, formal power series Categories:32A05, 26E05 
