Spectral Analysis of the Non-self-adjoint Mathieu-Hill Operator

Abstract

We obtain uniform, with respect to t asymptotic formulas for the eigenvalues of the operators generated in (0,1) by the Mathieu-Hill equation with a complex-valued potential and by the t-periodic boundary conditions. Then using it we investigate the non-self-adjoint Mathieu-Hill operator H generated in the allreal line by the same equation and establish the necessary and sufficient conditions for the potential for which H has no spectral singularity at infinity and it is an asymptotically spectral operator.

References in corpus (2)

• Isospectral Mathieu-Hill Operators
• Asymptotic formulas for spectral gaps and deviations of Hill and 1D Dirac operators

Cited by in corpus (5)

• On the spectral properties of the Schrodinger operator with a periodic PT-symmetric potential
• Isospectral Mathieu-Hill Operators
• On the Simplicity of the Eigenvalues of the Non-self-adjoint Mathieu-Hill Operators
• On the Spectral Singularities and Spectrality of the Hill Operator
• Spectral Expansion Series with Parenthesis for the Nonself-adjoint Periodic Differential Operators