Bounded Laplace transforms, primitives and semigroup orbits

Journal article

Let f : ℝ+ → ℂ be an exponentially bounded, measurable function whose Laplace transform has a bounded holomorphic extension to the open right half-plane. It is known that there is a constant C such that |∫0t f (s) ds| ≦ C (1 + t) for all t ≧ 0. We show that this estimate is sharp. Furthermore, the corresponding estimates for orbits of C0-semigroups are also sharp.

Authors: Batty, C

• Journal: Archiv der Mathematik
• Volume: 81
• Issue: 1
• Pages: 72-81
• Publication date: 2003-07-01
• DOI: 10.1007/s00013-003-0427-7
• EISSN: 1420-8938
• ISSN: 0003-889X
• Language: English