两个边界条件带谱参数的Sturm-Liouville算子特征的渐近分析

Asymptotic Analysis of A Class of Sturm-Liouville Operators with Spectral-parameter in Two Boundary Conditions

研究了一类具有转换条件且在两个边界条件中带谱参数的Sturm-Liouville算子特征的渐近式.将对上述问题特征值与特征函数的研究,转化为考虑定义在Hilbert空间H中一个算子A的特征值与特征函数问题,并通过对基本解的渐近分析求出特征值与相应特征函数的渐近式.

To investigate the asymptotic formulas of a class of Sturm-Liouville operators with transmission conditions and spectral-parameter in two boundary conditions. A self-adjoint linear operator A is defined in Hilbert space H such that the eigenvalues and eigenfunctions of such a problem are transformed into those of operator A. Apply the asymptotic analysis of a fundamental solution to find asymptotic formulae of eigenvalues and corresponding eigenfunctions.