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

Abstract

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 $D^{2m}u+Vu=\lambda u$, $D=-id/dx$, 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.

23 pages

References in corpus (2)

• Singular eigenvalue problems on the circle
• Estimates for Periodic Eigenvalues of the Differential Operator $(-1{)}^{\mathbf{m}}{\mathbf{d}}^{2m}/d{\mathbf{x}}^{2m}+\mathbf{V}$ with V -- Distribution

Cited by in corpus (2)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• Singularly perturbed periodic and semiperiodic differential operators