process admits the convolution type representation (2.1),(2.2). The kernel $k(y)$ is defined by relations (2.33) and (2.34).\
**Example 2.4.** The normal inverse Gaussian process .\
In the case of the normal inverse Gaussian process we have $A=0,\quad \gamma=\overline{\gamma}$ and $$\nu^{\prime}(y)=Ce^{\beta y}K_{1}(|y|)|y|^{-1},\quad C>0,\quad
-1{\leq}\beta{\leq}1,$$where $K_{\lambda}(x)$ denotes the modified Bessel function of the third kind with index the $\lambda$. Using equalities $$|K_{1}(|x|)|{\leq}Me^{-|x|}/|x|,\quad M>0,\quad
0<x_{0}{\leq}|x|,$$ $$|K_{1}(|x|)x|{\leq}M,\quad
0{\leq}|x|{\leq}x_{0}$$ we see that the conditions of Proposition 2.2 are fulfilled. Hence the corresponding generator $L$ admits the convolution type representation (2.1), (2.2) and the kernel $k(y)$ is defined by relations (2.33) and (2.34).\
**Example 2.5.** The Meixner process .\
For the Meixner process we have $$\nu^{\prime}(y)=C\frac{\mathrm{exp}{\beta}x}{x\,\mathrm{sinh}{\pi}x}
,$$where $C>0,\quad -\pi<\beta<\pi.$ The conditions of Proposition 2.2 are fulfilled. Hence the corresponding generator $L$ admits the convolution type representation (2.1),(2.2) and the kernel $k(y)$ is defined by relations (2.33),(2.34).\
**Remark 2.1.** Examples 2.1-2.5 are used in the finance problems \[24\].\
**Example 2.6.** Compound Poisson process.\
We consider the case when $A=0, \quad \gamma=0$ and $$M=\int_{-\infty}^{\infty}\nu^{\prime}(y)dy<\infty.$$ Using formulas (2.1) and (2.2) we deduce that the corresponding generator $L$ has the following convolution form $$Lf=-Mf(x)+\int_{-\infty}^{\infty}\nu^{\prime}(y-x)f(y)dy.$$

Potential
=========

The operator $$Qf=\int_{0}^{\infty}(P_{t}f)dt$$ is called *potential* of the semigroup $P_{t}$. The generator $L$ and 