Abstract
A well-known necessary and sufficient condition for the operator A to be the infinitesimal generator of a strongly continuous (C0) group is that both A and -A generate a C0-semigroup. This seems to imply that one has to check the conditions in the Hille-Yosida Theorem for both A and -A. In this paper we show that this is not necessary. Given that A generates a C0-semigroup we prove that a (weak) growth bound on the resolvent on a left half plane is sufficient to guarantee that A generates a group. This extends the recent result found by Liu, see [Liu98].
| Original language | English |
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| Title of host publication | European Control Conference, ECC 1999 - Conference Proceedings |
| Publisher | IEEE |
| Pages | 3432-3434 |
| Number of pages | 3 |
| ISBN (Electronic) | 9783952417355 |
| Publication status | Published - 24 Mar 2015 |
| Event | 1999 European Control Conference, ECC 1999 - Karlsruhe, Germany Duration: 31 Aug 1999 → 3 Sep 1999 |
Conference
| Conference | 1999 European Control Conference, ECC 1999 |
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| Abbreviated title | ECC |
| Country | Germany |
| City | Karlsruhe |
| Period | 31/08/99 → 3/09/99 |
Keywords
- Hilbert space
- strongly continuous group
- strongly continuous semigroup