On the Differential Operators with Periodic Matrix Coefficients

Details On the Differential Operators with Periodic Matrix Coefficients On the Differential Operators with Periodic Matrix Coefficients

2009-03-04

arxiv.org/abs/0903.0776v1

Mathematics

Spectral Theory

Scientific paper

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

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