基于 Wronski 行列式构建 Hilbert 函数空间中线性无关正交函数的方法
泛函分析
2026-05-19 v3
摘要
基于 Wronski 行列式，我们提出一种在任意 Hilbert 函数空间中构建线性无关正交函数的方法。该方法仅需要考虑函数空间中满足一定温和条件的初始函数，因而可视为 Gram-Schmidt 过程的一种推广。考虑了两种应用，包括求解常微分方程的解以及基函数的构建。我们还提出一种将后者与前者相联系的猜想， leading to the introduction of the Wronski basis.
引用
@article{arxiv.2508.04639,
title = {Construction of linearly independent and orthogonal functions in Hilbert function spaces via Wronski determinants},
author = {Athanasios Christou Micheas},
journal= {arXiv preprint arXiv:2508.04639},
year = {2026}
}
备注
20 pages; generalization of Gram-Schmidt orthonormalization; construction of basis functions; differential equations and Wronski basis; conjecture on bases in Hilbert spaces