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## Studia Mathematica

2008 | 187 | 3 | 199-218
Tytuł artykułu

### Convergence at the origin of integrated semigroups

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EN
Abstrakty
EN
We study a classification of κ-times integrated semigroups (for κ > 0) by their (uniform) rate of convergence at the origin: $||S(t)|| = 𝒪(t^{α})$ as t → 0 (0 ≤ α ≤ κ). By an improved generation theorem we characterize this behaviour by Hille-Yosida type estimates. Then we consider integrated semigroups with holomorphic extension and characterize their convergence at the origin, as well as the existence of boundary values, by estimates of the associated holomorphic semigroup. Various examples illustrate these results. The particular case α = κ, which corresponds to the notions of Riesz means or tempered integrated semigroups, is of special interest; as an application, it leads to an integrated version of Euler's exponential formula.
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Tom
Numer
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199-218
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wydano
2008
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autor
• Department of Theoretical Physics, University of Geneva, quai Ernest-Ansermet 24, CH-1211 Genève 4, Switzerland
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