The Abel summability of regularized traces (Q1596169)

The paper deals with the regularization of the sum of eigenvalues \(\mu_n\) of some operator \(A+B\): \[ \sum_{n=1}^\infty (\mu_n-\lambda_n-B_n)=S,\tag{1} \] where the \(\lambda_n\) are eigenvalues of the unperturbed operator \(A\), and the \(B_n\) are some numbers depending on the operators and ensuring the series convergence. The author derives new formulas for the abelian summation of the regularized traces of discrete operators~(1).