Uniform estimates for the semi-periodic eigenvalues of the singular differential operators

Let $m\in \mathbb{N}$, $\alpha \in [0,1]$, and $V$ be a 1-periodic complex-valued distribution in the negative Sobolev space $H^{-m\alpha }[0,1]$. The singular non-self-adjoint eigenvalue problem $D^{2m}u+Vu=\lambda u$, $D=-i d/dx$,withsemi-periodicboundaryconditionsisinvestigated\mathrm{.}Theuniformin$V$ asymptotic and non-asymptotic eigenvalue estimates are found and proved. The case of periodic boundary conditions was studied by authors earlier.