Slowly oscillating solutions of Cauchy problems with countable spectrum

Journal article

Let u be a bounded slowly oscillating mild solution of an inhomogeneous Cauchy problem, u̇(t) = Au(t) + f(t), on ℝ or ℝ+, where A is a closed operator such that σap(A) ∩ iℝ is countable, and the Carleman or Laplace transform of f has a continuous extension to an open subset of the imaginary axis with countable complement. It is shown that u is (asymptotically) almost periodic if u is totally ergodic (or if X does not contain c0 in the case of a problem on ℝ). Similar results hold for second-order Cauchy problems and Volterra equations.

Authors: Arendt, W; Batty, C

• Publication status: Published
• Journal: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
• Volume: 130
• Issue: 3
• Pages: 471-484
• Publication date: 2000-01-01
• ISSN: 0308-2105
• Language: English