有限秩移位高斯级数逼近的正确性
On the correctness of finite-rank approximations by series of shifted Gaussians
摘要：
本文研究了高斯整数移位级数的插值问题。这些问题的已知方法遇到了数值上的困难。由于它的另一种方法被认为是基于有限秩近似的线性系。这种方法的主要结果是建立所考虑的有限秩线性系的正确性。本文的主要结果是证明了有限秩线性系逼近的正确性。为此，推导出了线性系的主行列式的显式公式，证明了它是非零的。
英文摘要：
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations by linear systems. The main result for this approach is to establish correctness of the finite-rank linear system under consideration. And the main result of the paper is to prove correctness of the finite-rank linear system approximation. For that an explicit formula for the main determinant of the linear system is derived to demonstrate that it is non-zero.
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。
