2 problems

Let ${\bf L}^n$ be a self-adjoint operator defined by left-definite theory on $L^2[(a,b),w]$ with domain $\mathcal{D}_{\bf L}^n$ that includes a complete system of orthogonal polyn…

Let $n\in\mathbb{N}$. For a closed, densely defined operator $T$, write $D(T^k)$ for the domain of its $k$-th power and $D[T^{*k}]$ for the domain of the $k$-th power of its adjoin…