On smooth functions invariant relative to groups generated by reflections (Q1326085)

Let \(W\) be a finite group acting on \(\mathbb{R}^l\) generated by reflections and let \(p= (p_1,\dots, p_l)\) be a basis in the algebra of \(W\)-invariant polynomials. Every \(W\)-invariant function \(f\) on \(\mathbb{R}^l\) is of the form \(f(x)= F(p(x))\) for some function \(F\). The author studies the relationship between the smoothness of \(F\) and \(f\).