On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one
Abstract
It is shown that, if all weak solutions of the evolution equation equation* y'(t)=Ay(t),\ t0, equation* with a scalar type spectral operator A in a complex Banach space are Gevrey ultradifferentiable of orders less than one, then the operator A is necessarily bounded.
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