Local polynomial convexity of graphs of functions in several variables

Abstract

In this paper, we investigate the locally polynomial convexity of graphs of smooth functions in several variables. We also give a sufficient condition for a real analytic function g defined near 0 in C which behaves like z‾n near the origin so that the algebra generated by zm and g is dense in the space of continuous functions on D for all disks D close enough to the origin in C.