奇异非自伴Sturm-Liouville问题的谱包含与谱精确性

Selfadjoint and $m$ sectorial extensions of Sturm-Liouville operators

The self-adjoint and $m$-sectorial extensions of coercive Sturm-Liouville operators are characterised, under minimal smoothness conditions on the coefficients of the differential expression.

Eigenvalue estimates for singular left-definite Sturm-Liouville operators

The spectral properties of a singular left-definite Sturm-Liouville operator $JA$ are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart $A$ which is obtained by substituting the indefinite weight function by its absolute value. The spectrum of the $J$-selfadjoint operator $JA$ is real and it follows that an interval $(a,b)\subset\mathbb R^+$ is a gap in the essential spectrum of $A$ if and only if both intervals $(-b,-a)$ and $(a,b)$ are gaps in the essential spectrum of the $J$-selfadjoint operator $JA$. As one of the main results it is …

论非自伴Sturm-Liouville算子非局部扰动的恢复

On recovering non-local perturbation of non-selfadjoint Sturm-Liouville operator

本文研究非自伴Sturm-Liouville算子非局部扰动的逆谱问题，针对已知p的情形，通过建立特征函数与位势系数的关系，得到谱的充要条件，指出部分谱无信息，补充最小系数数据后证明了逆问题的唯一性并给出算法。

Discrete Fractional Sturm-Liouville Equations

In this study, we define discrete fractional Sturm-Liouville (DFSL) operators within Riemann-Liouville and Grünwald-Letnikov fractional operators with both delta and nabla operators. We show selfadjointness of the DFSL operator for the first time and prove some spectral properties, like orthogonality of distinct eigenfunctions, reality of eigenvalues, paralelly in integer and fractional order differential operator counterparts.

Random Sturm Liouville Operators

Selfadjoint Sturm-Liouville operators $H_ω$ on $L_2(a,b)$ with random potentials are considered and it is proven, using positivity conditions, that for almost every $ω$ the operator $H_ω$ does not share eigenvalues with a broad family of random operators and in particular with operators generated in the same way as $H_ω$ but in $L_2(\tilde a,\tilde b)$ where $(\tilde a,\tilde b)\subset(a,b)$.

Indefinite Sturm-Liouville operators $ (\sgn x) (- \frac{d^2}{dx^2} +q(x))$ with finite-zone potentials

The indefinite Sturm-Liouville operator $A = (\sgn x)(-d^2/dx^2+q(x))$ is studied. It is proved that similarity of $A$ to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of Weyl functions are given. For operators with a finite-zone potential, the components $\Aess$ and $\Adisc$ of $A$ corresponding to essential and discrete spectrums, respectively, are considered. A criterion of similarity of $\Aess$ to a selfadjoint operator is given in terms of Weyl functions for the Sturm-Liouville operator $-d^2/dx^2+q(x)$ with a finite-zo…