Name
Abstract | ||
|---|---|---|
Two conjectures on admissible control operators by George Weiss are disproved in this paper. One conjecture says that an operator B defined on an infinite-dimensional Hilbert space U is an admissible control operator if for every element u∈U the vector Bu defines an admissible control operator. The other conjecture says that B is an admissible control operator if a certain resolvent estimate is satisfied. The examples given in this paper show that even for analytic semigroups the conjectures do not hold. In the last section we construct a semigroup example showing that the first estimate in the Hille–Yosida theorem is not sufficient to conclude boundedness of the semigroup. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0167-6911(02)00277-3 | Systems & Control Letters |
Keywords | Field | DocType |
Infinite-dimensional system,Admissible control operator,Conditional basis,C0-semigroup | Hilbert space,Discrete mathematics,C0-semigroup,Resolvent,Operator (computer programming),Semigroup,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
48 | 3 | 0167-6911 |
Citations | PageRank | References |
7 | 1.67 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hans Zwart | 1 | 53 | 10.37 |
| Birgit Jacob | 2 | 7 | 2.01 |
| Olof J. Staffans | 3 | 66 | 15.08 |