Quantified versions of Ingham's theorem. (8th April 2016) - Chill, Ralph; Seifert, David
Abstract : 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 forC 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 so‐called 'fudge factor' appearing in proofs based on estimating contour integrals.