A representation of the transmutation kernels for the Schr\"odinger operator in terms of eigenfunctions and applications
Classical Analysis and ODEs
2018-12-31 v1 Analysis of PDEs
Numerical Analysis
Abstract
The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schr\"odinger operator with the second derivative are obtained in terms of the eigenfunctions of a corresponding Sturm-Liouville problem. Since both series converge slowly and in general only in a certain distributional sense we find a way to improve these expansions and make them convergent uniformly and absolutely by adding and subtracting corresponding terms. A numerical illustration of the obtained results is given.
Keywords
Cite
@article{arxiv.1812.10513,
title = {A representation of the transmutation kernels for the Schr\"odinger operator in terms of eigenfunctions and applications},
author = {Kira V. Khmelnytskaya and Vladislav V. Kravchenko and Sergii M. Torba},
journal= {arXiv preprint arXiv:1812.10513},
year = {2018}
}
Comments
10 pages, 2 figures