Numerical evaluation of operator determinants

Abstract

For any integral operator $K$ in the Schatten--von Neumann classes of compact operators and its approximated operator $K_N\sim (N\ge 1)$ obtained by using for example a quadrature or projection method, we show that the convergence of the approximate $p$-modified Fredholm determinants $\sideset{}{_{Np}}\det(I_N+zK_N)$ to the $p$-modified Fredholm determinants $\sideset{}{_p}\det(I_\mathcal{H}+zK)$ is uniform for all $p\ge 1$. As a result, we give the rate of convergences when evaluating at an eigenvalue or at an element of the resolvent set of $K$.

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References in corpus (1)

• On the Numerical Evaluation of Fredholm Determinants