英厄姆定理的量化形式
Quantified versions of Ingham's theorem
摘要：
我们获得量化版本的英厄姆的经典Tauberian定理和它的一些变种通过一个自然的修改英厄姆自己的简单证明。作为主要一般结果的推论，我们得到了$C_0$ -半群的量化衰减估计。结果重现那些已知的文献，但都更一般，在一种情况下，尖锐。他们也导致了更好地理解以前模糊的“捏造因素”出现在证明的基础上估计轮廓积分。
英文摘要：
We obtain quantified versions of Ingham's classical Tauberian theorem and some of its variants by means of a natural modification of Ingham's own simple proof. As corollaries of the main general results, we obtain quantified decay estimates for $C_0$-semigroups. The results reproduce those known in the literature but are both more general and, in one case, sharper. They also lead to a better understanding of the previously obscure "fudge factor' appearing in proofs based on estimating contour integrals.
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。
