Zero-class admissibility of observation operators
Abstract
An admissible observation operator is zero-class admissible if the norm of the output map tends to zero as the time tends to zero. Sufficient and necessary conditions for zero-class admissibility of observation operators are developed and a modified Weiss condition is studied. It is shown that the modified Weiss condition is in general necessary, but not sufficient for zero-class admissibility. For several important classes of C_0-semigroups it is proved that the modified Weiss condition is indeed equivalent to zero-class admissibility. The methods are illustrated by certain PDE examples.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2008
- DOI:
- 10.48550/arXiv.0810.0972
- arXiv:
- arXiv:0810.0972
- Bibcode:
- 2008arXiv0810.0972J
- Keywords:
-
- Mathematics - Functional Analysis;
- Mathematics - Optimization and Control;
- 93B07;
- 93B28 (Primary) 47D06;
- 47N70 (Secondary)
- E-Print:
- 12 pages