defined. The following statement will play a crucial role in our consideration.

\[pr3.2\] Under Hypothesis \[hyp1.1\], the right reflection coefficient given by exists and admits the representation $$R(\lambda )=A(\lambda )+\frac{S(\lambda )G(\lambda )}{\lambda B(\lambda )}
\label{Rep}$$where functions $A,B,S,G$ have the properties

1.  \[it1\] $A$ is an analytic on $\mathbb{C}^+\setminus[0,ih_0]$ function such that $\left\vert A \right\vert \le2$ on $\mathbb{R}$ and $A(\lambda)=o\left(1/\lambda\right)$, $\lambda\to\infty$ along any ray in $\mathbb{C}^+$

2.  \[it2\] $B$ is the Blaschke product $$B(\lambda )=\prod_{k=1}^{N}\frac{\lambda -i\varkappa _{k}}{\lambda
    +i\varkappa _{k}}$$where real $\varkappa _{k}$’s are such that $\left\{ -\varkappa
    _{k}^{2}\right\} _{k=1}^{N}$ is the negative discrete spectrum of $H_{q_{+}}$, $q_{+}\equiv q|_{\mathbb{R}_{+}}$

3.  \[it3\] $\left\vert S(\lambda )\right\vert \leq 1$, $\lambda \in 
    \mathbb{C}^{+}$

4.  \[it4\] $G\in G^{\frac{1}{\varepsilon }-1}$

5.  \[it5\] $\left\vert S(\lambda )G(\lambda )/\lambda \right\vert
    \leq 1$ a.e. on $\mathbb{R}$

6.  \[it6\] If $R_{n}$ is as in Definition \[def3.1\] then $$R_{n}(\lambda )=A_{n}(\lambda )+\frac{S(\lambda )G(\lambda )}{\lambda
    B(\lambda )}$$and $$A_{n}\rightarrow A,\;n\rightarrow \infty$$uniformly on any compact in $\mathbb{C}^{+}\setminus \lbrack 0,ih_{0}]$.

Most of statements in Proposition \[pr3.2\] (save ) are proven in [@Ry11] and we restrict ourselves to some comments only. Note first that Condition 1 of Hypothesis \[hyp1.1\] implies that $-\partial
_{x}^{2}+q(x)$ is in the limit point case at $-\infty $ (see, e.g. [ClarkGeszt03]{} for complete results on this 