Abstract
For the evolution equation y′(t) = Ay(t) with a scalar type spectral operator A in a Banach space, conditions on A are found that are necessary and sufficient for all weak solutions of the equation on [0, ∞) to be strongly infinite differentiable on [0, ∞) or [0, ∞). Certain effects of smoothness improvement of the weak solutions are analyzed.
Highlights
Consider the evolution equation y t Ay t1.1 with a scalar type spectral operator A in a complex Banach space X
Following 1, we understand by a weak solution of equation 1.1 on an interval 0, T
For scalar type spectral operators, there has been developed an operational calculus for Borel measurable functions defined on σ A 6, 7
Summary
1.1 with a scalar type spectral operator A in a complex Banach space X. Y t etAf, t ∈ 0, T , f ∈ D etA , 0≤t
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