Some Results on Ordinary Differential Operators with Periodic Coefficients

摘要

For a general ordinary differential operator $\mathcal{L}$ with periodiccoefficients we prove that the characteristic polynomial of the Floquet matrixis irreducible over the field of meromorphic functions. We also consider amultipoint eigenvalue problem and show that its eigenspaces are spanned by pureor generalized Floquet solutions. Finally, at the end of the paper we mentionsome relevant conjectures and open questions.