Transformation operators for impedance Sturm–Liouville operators on the line

In the Hilbert space $H:=L_2(\mathbb{R})$, we consider impedance Sturm--Liouville operator $T:H\to H$ generated by differential expression $ -p\frac{d}{dx}{\frac1{p^2}}\frac{d}{dx}p$, where function $p:\mathbb{R}\to\mathbb{R}_+$ is of bounded variation on $\mathbb{R}$ and $\inf_{x\in\mathbb{R}} p(x)>0$. Existence transformation for $T$ its properties are studied.
 paper, suggest an efficient parametrization p in term a real-valued measure $\mu\in \boldsymbol M$ via$p_\mu(x):= e^{\mu([x,\infty))}, x\in\mathbb{R}.$For M$, establish existence $T_\mu$, which constructed with $p_\mu$. Continuous dependence $T_\mu$ $\mu$ also proved. As consequence, deduce that unitarily equivalent to $T_0:=-d^2/dx^2$.