On solutions of linear equations with polynomial coefficients

Abstract

We show that a linear functional equation with polynomial coefficients need not admit an arc-analytic solution even if it admits a continuous semialgebraic one. We also show that such an equation need not admit a Nash regulous solution even if it admits an arc-analytic one.

Final (corrected) version, to appear in Ann. Polon. Math

References in corpus (2)

• Continuous rational functions on real and $p$-adic varieties
• Decomposition of sets in real algebraic geometry

Cited by in corpus (1)

• ${\mathcal{C}}^m$ solutions of semialgebraic or definable equations