Nodal sets and continuity of eigenfunctions of Kre\uı-Feller operators

Sze-Man Ngai, Meng-Ke Zhang, Wen-Quan Zhao

Let $\mu$ be a compactly supported positive finite Borel measure on ${\mathbb{R}}^d$. Let $0<{\lambda }_1\le {\lambda }_2\le \dots$ be eigenvalues of the Kre$\breve{ı}$n-Feller operator ${\Delta }_{\mu }$. We prove t…