In this work we prove that the eigenvalues of $n$-dimensional massive Dirac operator $\mathscr{D}_0 + V$, $n\ge2$, perturbed by a possibly non-Hermitian potential $V$, are localized in union two disjoint disks complex plane, provided $V$ is sufficiently small with respect to mixed norms $L^1_{x_j} L^\infty_{\widehat{x}_j}$, for $j\in\{1,\dots,n\}$. massless case, instead discrete spectrum empty...

Perturbations AT of a selfadjoint operator A by symmetric finite rank operators T from H2(A) to H−2(A) are studied. The finite dimensional family of selfadjoint extensions determined by AT is given explicitly.

This paper touches upon several traditional topics of 1D linear complex analysis including distribution of zeros of entire functions, completeness problem for complex exponentials and for other families of special functions, some problems of spectral theory of selfadjoint differential operators. Their common feature is the close relation to the theory of complex Fourier transform of compactly s...