On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree $-n$

We study the limit behavior of the spectral characteristics of truncated multidimensional integral operators whose kernels are homogeneous of degree $-n$ and invariant under the rotation group $SO(n)$. We prove that the limit of the $\varepsilon$-pseudospectra of the truncated operators $K_{\tau}$ as $\tau\to0$ is equal to the union of the $\varepsilon$-pseudospectra of the original operator $K$ and the “transposed” operator $\widetilde{K}$.