Under our assumptions the operator $$Bf=\int_{\Delta}\Phi(x,y)f(y)dy$$ is compact. It means that the operator $B$ has a discrete spectrum $\lambda_{j}\quad (j=1,2,...),\quad \lambda_{j}{\to}0.$ Hence, the corresponding truncated generator $L_{\Delta}$ has a discrete spectrum too. Using the results from the theory of the integral equations with the difference kernels we represent the quasi-potential $B$ in the explicit form.\
3.The probability $p(t,\Delta)$ of the Levy process remaining within the given domain $\Delta$ (ruin problem) is investigated in our paper (section 5). M.Kac \[11\] had obtained the first results of this type for symmetric stable processes. Later we transposed these results for the non-symmetric stable processes \[20\], \[22\]. In this paper we show that integro-differential equation of M.Kac type is true for all the Levy processes, which have a continuous density. M.Kac writes \[11\]: “We are led here to integro-differential equations which offer formidable analytic difficulties and which we were able to solve only in very few cases.” M. Kac was able to overcome these difficulties only for Cauchy processes. H.Widom \[30\] solved these equations for symmetric stable processes. Both symmetric and non-symmetric stable processes were investigated in our works \[19\]-\[22\]. Now we develop these results and transfer them on the wide class of the 