Equivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter
Equivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter
复制标题
DOI：
10.1016/j.jmaa.2003.11.025
复制
发表时间：
2004-03
影响因子：
1.3
通讯作者：
P. Binding;P. Browne;B. Watson
中科院分区：
文献类型：
--
作者：
P. Binding;P. Browne;B. Watson
对于有理 f，考虑 Sturm-Liouville 边值问题的三个反问题 -y″+qy=λy、y(0)cosα=y′(0)sinα 和 y′(1)=f(λ)y(1)。结果表明，Weyl m 函数唯一确定 α、f 和 q，并且又由不同 α 值的两个谱或普吕弗角唯一确定。为此，有必要产生关于渐近和振荡的直接结果，具有独立的兴趣。
Three inverse problems for a Sturm–Liouville boundary value problem −y″+qy=λy, y(0)cosα=y′(0)sinα and y′(1)=f(λ)y(1) are considered for rational f. It is shown that the Weyl m-function uniquely determines α, f, and q, and is in turn uniquely determined by either two spectra from different values of α or by the Prüfer angle. For this it is necessary to produce direct results, of independent interest, on asymptotics and oscillation.