All Questions

Let $\alpha(x) : \mathbb{R} \to (0,\infty)$ have bounded variation (BV) and suppose $\inf_{\mathbb{R}} \alpha > 0$. Consider the second order differential operator $$H : =-\partial_x (\alpha(x) \...

Let $D$ be an unbounded densely defined operator on a separable Hilbert space $H$. If $D$ is diagonalisable with all eigenvalues having finite multiplicity and growing towards infinity, does it follow ...