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arXiv · 1706.08014

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator

Marat V. Markin
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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.

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Marat V. Markin. 2017-06-25. On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator. https://arxiv.org/abs/1706.08014

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