$(7.4)$ and $(7.9)$, $(7.10)$ are valid.*\
2). *For some $m>0$ the inequality* $$\frac{m}{|x|^{2}}{\leq}\nu^{\prime}(x),\quad |x|{\leq}1$$ *is true.*\
3.$$\int_{-\infty}^{\infty}k(t)dt<\infty.$$ *Then the corresponding operator $B$ is strongly sectorial .*\
*Proof.* As it is known (see \[25\],Ch.1) the inequality $$|\int_{-\infty}^{\infty}k(t)\mathrm{sin}xtdt|{\leq}\frac{M}{|x|},
\quad M>0,\quad |t|{\geq}1$$ is valid. From formulas (7.11) and (7.26) we conclude that $$\int_{-\infty}^{\infty}k(t)\mathrm{cos}xtdt{\geq}\int_{-1/x}^{1/x}{\nu}^{\prime}(t)
\frac{1-\mathrm{cos}xt}{x^{2}}dt{\geq}\frac{N}{|x|},\quad N>0,\quad |x|{\geq}1.$$ It follows from (7.28) and (7.29) that $$-\frac{\pi}{2}\beta{\leq}\mathrm{arg}(Sf,f){\leq}\frac{\pi}{2}\beta, \quad 0<\beta<1.$$ Hence according to (7.18) relation (7.25) is valid . The proposition is proved.\
**Remark 7.2.** The variance damped processes (Example 2.2, $\alpha{\geq}1$), the normal inverse Gaussian process (Example 2.4.), the Meixner process (Example 2.5.) satisfy the conditions of Proposition 7.6. Hence the corresponding operators $B$ are strongly sectorial.\
**Proposition 7.7.** *Let conditions $(7.3), (7.4)$ and $(7.9)$, $(7.10)$ be fulfilled. If the operator $S$ has the form* $$Sf=Af+\int_{\Delta}k(x-t)f(t)dt,\quad A>0.$$ *Then the corresponding operator $B$ is strongly sectorial.*\
*Proof.* It is easy to see that for some $\beta<1$ relation (7.23) is true. According to relation (7.18) the corresponding operator $B$ is strongly sectorial.

Quasi-potential $B$, structure and properties
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Let us begin with the symmetric segment $\Delta=[-c,c]$.\
**Theorem 8.1.** (see\[22\],p.140) *Let the following conditions be fulfilled\
1. There exist the functions $N_{k}(x){\in}L^{p}(-c,c),\quad p>1$ which satisfy the equations $$SN_{k}=x^{k-1},\quad k=1,2.$$ 