In this paper, we establish a Tauberian theorem of Wiener–Ikehara type. As an application, we give a short proof of Blackwell’s renewal theorem of discrete case. We also establish a Dirichlet series version of Blackwell’s renewal theorem as another application.

中文翻译：

---

Wiener-Ikehara型的陶伯定理及其应用

在本文中，我们建立了Wiener–Ikehara型的Tauberian定理。作为应用，我们简短地证明了布莱克韦尔离散个案的更新定理。我们还建立了Blackwell更新定理的Dirichlet级数版本作为另一个应用程序。