The weighted Weiss conjecture and reproducing kernel theses for generalized Hankel operators
Författare
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.
Avdelning/ar
- Matematik (naturvetenskapliga fakulteten)
- Harmonic Analysis and Applications
Publiceringsår
2014
Språk
Engelska
Sidor
85-120
Publikation/Tidskrift/Serie
Journal of Evolution Equations
Volym
14
Issue
1
Dokumenttyp
Artikel i tidskrift
Förlag
Birkhäuser Verlag
Ämne
- Mathematics
Nyckelord
- One parameter semigroups
- admissibility
- Hardy space
- weighted Bergman
- space
- Hankel operators
- reproducing kernel thesis
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 1424-3199