On the spectra of multidimensional normal discrete Hausdorff operators

In this paper, the general case of normal discrete Hausdorff operators in L2(Double-struck capital Rd)$$ {L} circumflex 2\left({\mathrm{\mathbb{R}}} circumflex d\right) $$ is studied. The main result states that under some natural arithmetic condition, the spectrum of such an operator is rotationally invariant. Several special cases and applications are considered.