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

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

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