On the Hill's Operator with Matrix Potential

2005/08/15 by O. A. Veliev, Veliev, O. A.
Mathematics · #FOS: Mathematics #Spectral Theory (math.SP) #math.SP

paper · pdf · doi:10.48550/arxiv.math/0508254

12 pages

arxiv created 2005/08/15 · arxiv updated 2009/12/01

Abstract

In this article we obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the self-adjoint operator generated by a system of Sturm-Liouville equations with summable coefficients and the quasiperiodic boundary conditions. Then using these asymptotic formulas, we find the conditions on the potential for which the number of gaps in the spectrum of the Hill's operator with matrix potential is finite.

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