The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2

偏微分方程谱问题的解析近似与高精度求解应用

Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems

本文提出基于Delsarte变换算子构造的近似求解Sturm-Liouville方程谱问题的方法，通过有限线性组合广义波多项式近似势函数原函数，实现高精度求解本征值和本征向量。

Construction of transmutation operators and hyperbolic pseudoanalytic functions

A representation for integral kernels of Delsarte transmutation operators is obtained in the form of a functional series with the exact formulas for the terms of the series. It is based on the application of hyperbolic pseudoanalytic function theory and recent results on mapping properties of the transmutation operators. The kernel $K_1$ of the transmutation operator relating $A=-\frac{d^2}{dx^2}+q_1(x)$ and $B=-\frac{d^2}{dx^2}$ results to be one of the complex components of a bicomplex-valued hyperbolic pseudoanalytic function satisfying a Vekua-type hyperbolic equation of a special form. Th…

本征值问题中的变换与谱参数幂级数

Transmutations and spectral parameter power series in eigenvalue problems

本文综述了Sturm-Liouville理论中关于变换算子和谱参数幂级数方法的最新进展，并介绍了递归积分系统及其在谱问题中的应用。