论文标题
Sturm-Liouville操作员的相对振荡理论和基本光谱
Relative oscillation theory and essential spectra of Sturm--Liouville operators
论文作者
论文摘要
我们为形式的一般sturm-liouville差异表达式开发了相对振荡理论\ [ \ frac {1} {r} \ left（ - \ frac {\ mathrm d} {\ mathrm dx} p \ frac {\ mathrm d} {\ mathrm d} {\ mathrm dx} + q \ right）\]＆prove扰动结果和$ pr的$ pp $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ p。这里的新颖之处在于，我们还允许重量功能$ r $扰动在这种情况下，在不同的希尔伯特空间中不受干扰和扰动的操作员行为。
We develop relative oscillation theory for general Sturm-Liouville differential expressions of the form \[ \frac{1}{r}\left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm dx} + q\right) \] and prove perturbation results and invariance of essential spectra in terms of the real coefficients $p$, $q$, $r$. The novelty here is that we also allow perturbations of the weight function $r$ in which case the unperturbed and the perturbed operator act in different Hilbert spaces.
