Spectrality of ordinary differential operators

关于具周期系数微分算子的谱性

On the Spectrality of the Differential Operators with Periodic Coefficients

本文研究了具周期复值系数的微分算子，提出了一个关于系数的条件，使得该算子成为Dunford意义下的谱算子。

Some Results on Ordinary Differential Operators with Periodic Coefficients

For a general ordinary differential operator $\mathcal{L}$ with periodic coefficients we prove that the characteristic polynomial of the Floquet matrix is irreducible over the field of meromorphic functions. We also consider a multipoint eigenvalue problem and show that its eigenspaces are spanned by pure or generalized Floquet solutions. Finally, at the end of the paper we mention some relevant conjectures and open questions.

The characterization problem for one class high order ordinary differential operators with periodic coefficients

The main purpose of the present work is solving the characterization problem which consist of identification of necessary and sufficient conditions on the scattering data ensuring that the reconstructed potential belongs to a particular class

Necessary and sufficient conditions for the inverse problem of one class ordinary differential operators with complex periodic coefficients

The basic purpose of the present paper is the full solutions of the inverse problem (i.e. a finding of necessary and sufficient conditions) for the operator with complex periodic coefficients.

Spectral functions of the simplest even order ordinary differential operator

We consider the minimal differential operator A generated in $L^2(0,\infty)$ by the differential expression $l(y) = (-1)^n y^{(2n)}$. Using the technique of boundary triplets and the corresponding Weyl functions, we find explicit form of the characteristic matrix and the corresponding spectral function for the Friedrichs and Krein extensions of the operator A.

On the Approximation of Isolated Eigenvalues of Ordinary Differential Operators

We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm-Liouville and Dirac operators by the eigenvalues of regular operators.