Singular eigenvalue problems on the circle

Abstract

The eigenvalue problem on the circle for the non-self-adjoint operators $L_m(V)=(-1{)}^m\frac{d^{2m}}{d{x}^{2m}}+V$, $m\in \mathbb{N}$ with singular complex-valued 2-periodic distributions $V\in H_{per}^{-m}[-1,1]$ is studied. Asymptotic formulae for the eigenvalues uniformly in $V$ in the space $H_{per}^m[-1,1]$ and local uniformly in $V$ in the space $H_{per}^{-m}[-1,1]$ are found.

7 pages

References in corpus (1)

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