On Completeness of the Products of Harmonic Functions
A. G. Ramm · Proceedings of the American Mathematical Society · 1986
Let $L$ be a partial differential operator in ${R^n}$ with constant coefficients. We prove that, under some assumption on $L$, the set of products of the elements of the null-space of $L$ forms a complete set in ${L^p}(D)$, $p \geqslant 1$, where $D$ is any bounded domain. In particular, the products of harmonic functions form a complete set in ${L^p}(D)$, $p \geqslant 1$.