Quantified versions of Ingham's theorem. (8th April 2016)

• Record Type: Journal Article
• Authors: Chill, Ralph; Seifert, David
• Is Part Of: Bulletin of the London Mathematical Society. Volume 48:Part 3(2016:Jun.)
• Page Start: 519
• Page End: 532
• Publication Date: 2016-04-08
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms/bdw024
• Languages: English
• ISSNs: 0024-6093

Abstract

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.