On the Asymptotic Behavior of Alexandrov’s $$n$$-Width of the Compact Set of Infinitely SmoothPeriodic Functions in a Gevrey Class

We consider the compact set of $$C^\infty $$ -smooth periodic functions in a Gevrey class that admits a bounded embedding into the space of continuous functions on the unit circle. We describe the asymptotic behavior of Alexandrov’s $$n $$ -width of this compact set.