Timeline for On exponential formula for $C_0$ semigroups
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2013 at 14:08 | vote | accept | driss-alamilouati | ||
| Feb 27, 2013 at 17:23 | |||||
| Feb 13, 2013 at 11:56 | comment | added | Delio Mugnolo | Wouldn't this imply norm continuity (and hence boundedness of the generator)? | |
| Feb 13, 2013 at 6:13 | comment | added | driss-alamilouati | Thank you for responding. Let me point out that P.loreti and A.Siconolfi (Semigoup approach for approximation of a control problem with unbounded dynamic) have shown convergence in norm uniformly for $C_0$-semigroups on the compact subsets of $(0,+\infty)$ when $X$ is a Hilbert space. I would like to have this propertie on the compact subsets of $[0,+\infty)$. N.B /I will be satisfied if $X$ is a Hilbert space. | |
| Feb 12, 2013 at 17:33 | comment | added | Delio Mugnolo | thanks, I did not know abouth that result by Le Roux. Are you aware of some similar results for $C_0$-groups or for cosine families? | |
| Feb 12, 2013 at 13:08 | comment | added | András Bátkai | Cachia is about Euler for not $C_0$-semigroups. Chachia and Zagrebnov and Blunck was more about rates of convergence for Trotter. The operator norm convergence of Euler for analytic semigroups was well-known in the 70's (Le Roux). | |
| Feb 12, 2013 at 12:07 | comment | added | Delio Mugnolo | uh? Andras, I do not understand. Have you checked those articles? E.g., Corollary 3.6 in Cachia's paper is clearly about Euler's formula and has nothing to do with Trotter. Btw, it is interesting to observe that for Trotter's product formula you can have even better convergence, e.g., trace norm convergence (this has been proved by Cachia and Zagrebnov) if you are in a Hilbert space, and the same holds for other relevant convergent sequences (e.g., the Dyson-Phillips formula), but I have never seen trace class convergence for the Euler formula. | |
| Feb 12, 2013 at 11:07 | comment | added | András Bátkai | They are about the Trotter product formula, not about Euler. | |
| Feb 12, 2013 at 10:55 | comment | added | Delio Mugnolo | sorry, I meant: by Blunck and Cachia. | |
| Feb 12, 2013 at 10:55 | comment | added | Delio Mugnolo | Yes, András. I have not checked exactly, but I kind of remember that the results by Blunck and Zagrebnov even generalize those by Crouzeix & co. you have referred to. | |
| Feb 12, 2013 at 10:33 | comment | added | András Bátkai | Delio, it is always true for analytic semigroups. See my answer I posted earlier. | |
| Feb 12, 2013 at 10:19 | history | answered | Delio Mugnolo | CC BY-SA 3.0 |