The weighted Weiss conjecture and reproducing kernel theses for generalized Hankel operators
Author
Summary, in English
The weighted Weiss conjecture states that the system theoretic property of weighted admissibility can be characterized by a resolvent growth condition. For positive weights, it is known that the conjecture is true if the system is governed by a normal operator; however, the conjecture fails if the system operator is the unilateral shift on the Hardy space (discrete time) or the right-shift semigroup on (continuous time). To contrast and complement these counterexamples, in this paper, positive results are presented characterizing weighted admissibility of linear systems governed by shift operators and shift semigroups. These results are shown to be equivalent to the question of whether certain generalized Hankel operators satisfy a reproducing kernel thesis.
Department/s
- Mathematics (Faculty of Sciences)
- Harmonic Analysis and Applications
Publishing year
2014
Language
English
Pages
85-120
Publication/Series
Journal of Evolution Equations
Volume
14
Issue
1
Document type
Journal article
Publisher
Birkhäuser Verlag
Topic
- Mathematics
Keywords
- One parameter semigroups
- admissibility
- Hardy space
- weighted Bergman
- space
- Hankel operators
- reproducing kernel thesis
Status
Published
Research group
- Harmonic Analysis and Applications
ISBN/ISSN/Other
- ISSN: 1424-3199