On linear inequality systems with smooth coefficients (Q1777594)

The authors consider linear inequality systems of the form \(\sigma=\{a_t\,x\geq b_t,\;t\in T\}\), where \(T\subset\mathbb{R}\) is compact, and \(b_t=b(t)\in\mathbb{R}\), \(a_t=a(t)=(a_1(t),\dots,a_n(t))\in\mathbb{R}^n\) are polynomial (resp. analytical) functions. Sufficient conditions are given for certain subsets \(F\) of \(\mathbb{R}^n\) to be solutions of an analytical or polynomial system. Several examples are given as applications of the characterizations obtained.