基于 Bohr 等价关系的几乎周期函数
复变函数
2019-03-18 v2
摘要
本文在实数或复变量的几乎周期函数类上引入一种等价关系，用以细化刻画这些函数空间的 Bochner 结果。事实上，关于一致收敛拓扑，我们证明了几乎周期函数的平移族之极限点恰为与之等价的函数，由此得到几乎周期性的一个刻画。特别地，我们证明了任何与 Riemann zeta 函数 等价的指数和，都可在 中由 的某些竖直平移一致逼近。
引用
@article{arxiv.1801.08035,
title = {Almost Periodic Functions in terms of Bohr's Equivalence Relation},
author = {J. M. Sepulcre and T. Vidal},
journal= {arXiv preprint arXiv:1801.08035},
year = {2019}
}
备注
This is a modified version of our homonymous paper published in Ramanujan J. (2018). As we pointed out in our corrigendum (2019), we correct a gap found in the original version which is due to a property that does not generally hold, but it does under the assumption of existence of an integral basis. The earlier equivalence relation is revised to adapt correctly the situation in the general case. arXiv admin note: text overlap with arXiv:1711.04122