复值势的重建技术
Reconstruction techniques for complex potentials
AI总结：
本文基于Bessel函数Neumann级数表示，将复值势Sturm-Liouville方程的逆系数问题转化为线性代数方程组，通过前两个系数恢复势，并给出高效数值算法。
摘要：
本文提出一种求解Sturm-Liouville方程 -y''+q(x)y=λy 的多种逆系数问题的方法，其中势q(x)为复值。该方法基于解的Bessel函数Neumann级数表示。借助这些表示，问题被约化为关于表示系数的线性代数方程组。势由前两个系数的算术组合恢复。所考虑问题的特殊情形包括从Weyl函数恢复势、逆双谱Sturm-Liouville问题以及有限区间上的逆散射问题。该方法可导出求解系数逆问题的高效数值算法。数值效率通过若干算例加以说明。
英文摘要：
An approach for solving a variety of inverse coefficient problems for the Sturm-Liouville equation -y''+q(x)y=λy with a complex valued potential q(x) is presented. It is based on Neumann series of Bessel functions representations for solutions. With their aid the problem is reduced to a system of linear algebraic equations for the coefficients of the representations. The potential is recovered from an arithmetic combination of the first two coefficients. Special cases of the considered problems include the recovery of the potential from a Weyl function, inverse two-spectra Sturm-Liouville problems, as well as the inverse scattering problem on a finite interval. The approach leads to efficient numerical algorithms for solving coefficient inverse problems. Numerical efficiency is illustrated by several examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
