On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: a constructive approach

一个一般化的定量 Ingham-Karamata Tauber 定理

A general quantified Ingham-Karamata Tauberian theorem

本文提出一个一般化的定量 Ingham-Karamata Tauber 定理，采用灵活单边条件，改进 Stahn 定理并证明速率在几乎所有情形下最优。

关于一类具有整 Laplace 变换的函数空间及其与 Ingham–Karamata 定理最优性的联系

On a space of functions with entire Laplace transforms and its connection with the optimality of the Ingham-Karamata theorem

本文研究一类 Laplace 变换可整延拓的连续可微函数所构成的 Fréchet 空间的逼近性质，并利用其与开映射定理证明 Ingham–Karamata Tauberian 定理的最优性。

Note on the absence of remainders in the Wiener-Ikehara theorem

We show that it is impossible to get a better remainder than the classical one in the Wiener-Ikehara theorem even if one assumes analytic continuation of the Mellin transform after subtraction of the pole to a half-plane. We also prove a similar result for the Ingham-Karamata theorem.

Optimality of the quantified Ingham-Karamata theorem for operator semigroups with general resolvent growth

We prove that a general version of the quantified Ingham-Karamata theorem for $C_0$-semigroups is sharp under mild conditions on the resolvent growth, thus generalising the results contained in a recent paper by the same authors. It follows in particular that the well-known Batty-Duyckaerts theorem is optimal even for bounded $C_0$-semigroups whose generator has subpolynomial resolvent growth. Our proof is based on an elegant application of the open mapping theorem, which we complement by a crucial technical lemma allowing us to strengthen our earlier results.