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On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator (1706.08014v4)
Published 25 Jun 2017 in math.FA
Abstract: Found are conditions on a scalar type spectral operator $A$ in a complex Banach space necessary and sufficient for all weak solutions of the evolution equation \begin{equation*} y'(t)=Ay(t),\ t\ge 0, \end{equation*} to be strongly Gevrey ultradifferentiable of order $\beta\ge 1$, in particular analytic or entire, on $[0,\infty)$. Certain inherent smoothness improvement effects are analyzed.