called *sectorial* if $$(Bf,f){\ne}0,\quad f{\ne}0$$ and $$-\frac{\pi}{2}\beta{\leq}\mathrm{arg}(Bf,f){\leq}\frac{\pi}{2}\beta, \quad 0<\beta{\leq}1.$$ It is easy to see that the following assertions are true.\
**Proposition 7.1.** *Let the operator $B$ be sectorial. Then the operator $(I+sB)^{-1}$ is bounded when* $s{\geq}0$.\
**Proposition 7.2.** *Let the conditions of Theorem $5.2$ be fulfilled. If the operator $B$ is sectorial, then formula $(5.23)$ is valid for all* $s{\geq}0.$\
In the present section we deduce the conditions under which the quasi-potential $B$ is sectorial. Let us consider the case when $$\int_{x}^{\infty}y{\nu}^{\prime}(y)dy<\infty,\quad (x>0),$$ $$\int_{-\infty}^{x}|y|{\nu}^{\prime}(y)dy<\infty,\quad (x<0).$$ The corresponding kernel $k(x)$ of the operator $S$ (see(2.2) has the form $$k(x)=\int_{x}^{\infty}(y-x){\nu}^{\prime}(y)dy<\infty,\quad (x>0),$$ $$k(x)= \int_{-\infty}^{x}(x-y){\nu}^{\prime}(y)dy<\infty,\quad (x<0).$$ Using the inequality ${\nu}^{\prime}(y){\geq}0$ we obtain the following statement.\
**Proposition 7.3.** *Let conditions $(7.3)$ and $(7.4)$ be fulfilled . Then the kernel $k(x)$ is monotone on the half-axis $(-\infty,0)$ and on the half-axis* $(0,\infty)$.\
We shall use the following Pringsheim’s result .\
**Theorem 7.1.** (see\[25\], Ch.1) *Let $f(t)$ be non-increasing function over $(0,\infty)$ and integrable on any finite interval* $(0,\ell)$. *If $f(t){\to}0$ when $t{\to}\infty$, then for any positive $x$ we have* $$\frac{1}{2}[f(x+0)+f(x-0)]=\frac{2}{\pi}\int_{+0}^{\infty}\mathrm{cos}xu
[\int_{0}^{\infty}f(t)\mathrm{cos}tudt]du,$$ $$\frac{1}{2}[f(x+0)+f(x-0)]=\frac{2}{\pi}\int_{0}^{\infty}\mathrm{sin}xu
[\int_{0}^{\infty}f(t)\mathrm{sin}tudt]du.$$ It follows from (7.3)-(7.6) that $$k(x){\to}0 \quad and \quad k^{\prime}(x){\to}0,\quad
when\quad x{\to}{\pm}\infty.$$ We suppose in addition that $$xk(x){\to}0 \quad and \quad x^{2}k^{\prime}(x){\to}0,\quad
when\quad 