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

2012/02/21 by Veliev, O. A. · 1 citation
#34L05 #34L20 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1202.4735

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.

Cited by

• On the Spectral Singularities and Spectrality of the Hill Operator

Related

• On the Spectrality and Spectral Expansion of the Non-self-adjoint\n Mathieu-Hill Operator in All Real Line
• Asymptotic Analysis of Non-self-adjoint Hill Operators
• On the Simplicity of the Eigenvalues of the Non-self-adjoint Mathieu-Hill Operators
• On the Hill's Operator with Matrix Potential
• On half-line spectra for a class of non-self-adjoint Hill operators