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A note on the spectral operators of scalar type and semigroups of bounded linear operators

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  • Marat V. Markin

Abstract

It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C 0 - and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator.

Suggested Citation

  • Marat V. Markin, 2002. "A note on the spectral operators of scalar type and semigroups of bounded linear operators," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 32, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:795412
    DOI: 10.1155/S0161171202112221
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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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