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In this chapter, we introduce the notion of the generator of a given bi-continuous semigroup. Moreover, we show that this generator has nice properties as they are also known from the strongly continuous case. For that, we also show that the resolvent of the generator can be represented by the Laplace transform of the semigroup.

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The Generator of Bi-continuous Semigroups

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  • 发表日期：

    2026年

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  • Christian Budde

摘要

In this chapter, we introduce the notion of the generator of a given bi-continuous semigroup. Moreover, we show that this generator has nice properties as they are also known from the strongly continuous case. For that, we also show that the resolvent of the generator can be represented by the Laplace transform of the semigroup.