We prove that linear almost periodic systems always carry almost automorphic dynamics, thus confirming in this case a more general conjecture by Shen and Yi. The result is based on the accurate description of the breakdown of the Favard separation condition.
Almost automorphic linear dynamics by Favard theory / J. Campos, M. Tarallo. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 256:4(2014), pp. 1350-1367. [10.1016/j.jde.2013.10.018]
Almost automorphic linear dynamics by Favard theory
M. Tarallo
2014
Abstract
We prove that linear almost periodic systems always carry almost automorphic dynamics, thus confirming in this case a more general conjecture by Shen and Yi. The result is based on the accurate description of the breakdown of the Favard separation condition.
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