This is the abstract of the paper
  "A new proof for a Barbasin's theorem in the periodic case"
by C. Buse and M. Giurgiulescu.

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Abstract: It is proved that a $q$-periodic evolutionary process
${\cal U}=\{U(t, s)\}_{t\ge s}$ of bounded linear operators on a Banach space
$X$ is uniformly exponentially stable if and only if the function
 $t\mapsto ||U(0, -t)||$ belongs to $L^1({\bf R}_+).$ We would use this
result for a new proof of a Barba\c sin's theorem in this particular case.

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