Zero-class admissibility of observation operators

Details Zero-class admissibility of observation operators Zero-class admissibility of observation operators

2008-10-06

arxiv.org/abs/0810.0972v1

Mathematics

Functional Analysis

12 pages

Scientific paper

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.

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