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

O. A. Veliev

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arXiv · 1202.4735

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

O. A. Veliev

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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.

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BibTeX RIS

O. A. Veliev. 2012-02-21. Spectral Analysis of the Non-self-adjoint Mathieu-Hill Operator. https://arxiv.org/abs/1202.4735

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