8 problems

Absolutely continuous sufficiency conjecture. Under these assumptions, the conditions and are sufficient for $A$ to be similar to a selfadjoint operator.

Hilbert-transform sufficiency conjecture. The estimates and should be sufficient for $A$ to be similar to a selfadjoint operator. Consequently, the similarity problem would reduce…

Let $T_q$ and $T_{\tilde{q}}$ be Sturm–Liouville operators with potentials $q$ and $\tilde{q}$ on $[0,\pi]$. Suppose that they have the same Weyl class. Weyl-class uniqueness conje…

Let ${\bf L}^n_0$, with $n\in\mathbb{N}$, be a self-adjoint extension of the minimal operator $L^n_{\scriptstyle \text{min}}$ on $L^2[(a,b),w]$, with deficiency indices $(m,m)$ whe…

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…

Left-definite domain equality conjecture. For every $n\in\mathbb{N}$,

Let $p$ be a positive parametrizing function, let $A_p$ be the associated Sturm–Liouville operator, and let $PW_{[0,\Omega]}(A_p)$ denote its spectral subspace. For a set $X$, writ…

Let $T$ be the selfadjoint operator associated with a singular Sturm–Liouville expression, and let $A$ be the corresponding indefinite Sturm–Liouville operator. Spectral lower-boun…