Abstract

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.

中文翻译：

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用移位高斯级数的有限秩逼近的正确性。

摘要

在本文中，我们考虑了通过高斯整数移位与级数相关的插值问题。解决这些问题的已知方法遇到了数字困难。因此，考虑了基于线性系统的有限秩近似的另一种方法。这种方法的主要结果是确定所考虑的有限秩线性系统的正确性。并且本文的主要结果是证明有限秩线性系统近似的正确性。为此，推导了线性系统主要行列式的显式公式，以证明它不是零。