论文标题
具有集成电位的狄拉克系统解决方案的渐近行为
Asymptotic behavior of solutions of the Dirac system with an integrable potential
论文作者
论文摘要
我们将dirac系统在\ mathbb {c} $中的频谱参数$μ\和带有$ l_p [0,1] $的条目的复杂值的电位上的间隔$ [0,1] $上考虑，其中$ 1 \ leq p <2 $。我们在条纹$ | {\ rm im} \，μ| \ le d $ for $μ\ to \ infty $中研究其解决方案的渐近行为。这些结果使我们能够获得与上述迪拉克系统相关的sturm--liouville操作员的特征值和特征函数的尖锐渐近公式。
We consider the Dirac system on the interval $[0,1]$ with a spectral parameter $μ\in\mathbb{C}$ and a complex-valued potential with entries from $L_p[0,1]$, where $1\leq p <2$. We study the asymptotic behavior of its solutions in a stripe $|{\rm Im}\,μ|\le d$ for $μ\to \infty$. These results allows us to obtain sharp asymptotic formulas for eigenvalues and eigenfunctions of Sturm--Liouville operators associated with the aforementioned Dirac system.
