On an abstract evolution equation with a spectral operator of scalar type

Marat V. Markin

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 32, 1-9

Abstract:

It is shown that the weak solutions of the evolution equation y ′ ( t ) = A y ( t ) , t ∈ [ 0 , T ) ( 0 < T ≤ ∞ ) , where A is a spectral operator of scalar type in a complex Banach space X , defined by Ball (1977), are given by the formula y ( t ) = e t A f , t ∈ [ 0 , T ) , with the exponentials understood in the sense of the operational calculus for such operators and the set of the initial values, f 's, being ∩ 0 ≤ t < T D ( e t A ) , that is, the largest possible such a set in X .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:813143

DOI: 10.1155/S0161171202112233

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