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arXiv · 1707.09359

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the open semi-axis

Marat V. Markin
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Abstract

Given the abstract evolution equation \[ y'(t)=Ay(t),\ t\ge 0, \] with scalar type spectral operator $A$ in a complex Banach space, found are conditions necessary and sufficient for all weak solutions of the equation, which a priori need not be strongly differentiable, to be strongly Gevrey ultradifferentiable of order $\beta\ge 1$, in particular analytic or entire, on the open semi-axis $(0,\infty)$. Also, revealed is a certain interesting inherent smoothness improvement effect.

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Marat V. Markin. 2017-06-29. On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the open semi-axis. https://arxiv.org/abs/1707.09359

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