On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one. (English) Zbl 1506.34076
Summary: It is shown that, if all weak solutions of the evolution equation
\[y'(t)=Ay(t),\, t\ge 0,\]
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.
MSC:
| 34G10 | Linear differential equations in abstract spaces |
| 47B40 | Spectral operators, decomposable operators, well-bounded operators, etc. |
| 30D15 | Special classes of entire functions of one complex variable and growth estimates |
| 47B15 | Hermitian and normal operators (spectral measures, functional calculus, etc.) |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47D60 | \(C\)-semigroups, regularized semigroups |
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