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**On the differential operators with periodic matrix coefficients.**
*(English)*
Zbl 1195.34134

Following his earlier work [Math. Nachr. 281, 1341–1350 (2008; Zbl 1168.34054)] on the special case \(n=2\), the author obtains asymptotic formulae for eigenvalues and eigenfunctions of a system of \(n\)th order linear ordinary differential equations with summable (not necessarily continuous) complex-valued coefficients with quasiperiodic boundary conditions. These are used to find conditions on the coefficients for which the number of gaps in the spectrum of a self-adjoint differential operator with periodic coefficients is finite.

Reviewer: Alan L. Andrew (Bundoora)

### MSC:

34L20 | Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators |

47E05 | General theory of ordinary differential operators |

34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |

34L05 | General spectral theory of ordinary differential operators |

### Citations:

Zbl 1168.34054### References:

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