# Journal article

## Slowly oscillating solutions of Cauchy problems with countable spectrum

Abstract:
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.
Publication status:
Published

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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
Pubs id:
pubs:932
UUID:
uuid:3717bbb1-f506-4ba4-b48b-c622c5846739
Local pid:
pubs:932
Source identifiers:
932
Deposit date:
2012-12-19