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

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  • Marat V. Markin

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 .

Suggested Citation

  • Marat V. Markin, 2002. "On an abstract evolution equation with a spectral operator of scalar type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 32, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:813143
    DOI: 10.1155/S0161171202112233
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    Cited by:

    1. Marat V. Markin, 2018. "On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator on the Real Axis," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-14, July.

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