On substantiation of a method for calculation of nuclear operators' eigenvalues with the help of the theory of traces

We justify the existence of eigenvalues $\{\lambda_n\}_{n=1}^{\infty}$ of the nuclear operator $T$ inside the circle $|x-\mu|\leq r$ on the complex plane with the centre at the point $\mu$, where $\mu$ is determined as formal number of the operator $T$ and $r$ is the exponent of $\mu$.