| Title:
|
A universal property of $C_0$-semigroups (English) |
| Author:
|
Herzog, Gerd |
| Author:
|
Schmoeger, Christoph |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
83-88 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $T:[0, \infty) \to L(E)$ be a $C_0$-semigroup with unbounded generator $A:D(A)\to E$. We prove that $(T(t)x-x)/t$ has generically a very irregular behaviour for $x\notin D(A)$ as $t \to 0+$. (English) |
| Keyword:
|
$C_0$-semigroups |
| Keyword:
|
universal elements |
| MSC:
|
47D06 |
| MSC:
|
54H99 |
| idZBL:
|
Zbl 1212.47018 |
| idMR:
|
MR2562805 |
| . |
| Date available:
|
2009-08-18T12:23:12Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133416 |
| . |
| Reference:
|
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| Reference:
|
[2] Grosse-Erdmann K.-G.: Universal families and hypercyclic operators.Bull. Amer. Math. Soc. (N.S.) 36 (1999), 345--381. Zbl 0933.47003, MR 1685272, 10.1090/S0273-0979-99-00788-0 |
| Reference:
|
[3] Herzog G., Lemmert R.: On Hölder continuous universal primitives.Bull. Korean Math. Soc, to appear. Zbl 1163.26304, MR 2502799 |
| Reference:
|
[4] Marcinkiewicz J.: Sur les nombres dérivés.Fund. Math. 24 (1935), 305--308. Zbl 0011.10705 |
| Reference:
|
[5] Pazy A.: Semigroups of Linear Operators and Applications to Partial Differential Equations.Applied Mathematical Sciences, 44, Springer, New York, 1983. Zbl 0516.47023, MR 0710486 |
| Reference:
|
[6] Taylor A.E., Lay D.C.: Introduction to Functional Analysis.second edition, John Wiley & Sons, New York-Chichester-Brisbane, 1980. Zbl 0654.46002, MR 0564653 |
| Reference:
|
[7] Wilansky A.: Modern Methods in Topological Vector Spaces.McGraw-Hill International Book Co., New York, 1978. Zbl 0395.46001, MR 0518316 |
| . |
