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Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0-semigroup are found, the latter formulated exclusively in terms of the operator's spectrum

international journal of mathematics and mathematical sciences

On scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiable<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$C_0$"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math>-semigroups

On scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiableC0-semigroups