The weighted Weiss conjecture and reproducing kernel theses for generalized Hankel operators
(2014) In Journal of Evolution Equations 14(1). p.85-120- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4417627
- author
- Jacob, B.
; Rydhe, Eskil
LU
and Wynn, A.
- organization
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- One parameter semigroups, admissibility, Hardy space, weighted Bergman, space, Hankel operators, reproducing kernel thesis
- in
- Journal of Evolution Equations
- volume
- 14
- issue
- 1
- pages
- 85 - 120
- publisher
- Birkhäuser
- external identifiers
-
- wos:000332084600004
- scopus:84894672598
- ISSN
- 1424-3199
- DOI
- 10.1007/s00028-013-0209-z
- language
- English
- LU publication?
- yes
- id
- b348ae9d-c5e8-4cf9-9724-5d427d9bcb16 (old id 4417627)
- date added to LUP
- 2016-04-01 09:52:55
- date last changed
- 2024-08-11 07:57:34
@article{b348ae9d-c5e8-4cf9-9724-5d427d9bcb16, abstract = {{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.}}, author = {{Jacob, B. and Rydhe, Eskil and Wynn, A.}}, issn = {{1424-3199}}, keywords = {{One parameter semigroups; admissibility; Hardy space; weighted Bergman; space; Hankel operators; reproducing kernel thesis}}, language = {{eng}}, number = {{1}}, pages = {{85--120}}, publisher = {{Birkhäuser}}, series = {{Journal of Evolution Equations}}, title = {{The weighted Weiss conjecture and reproducing kernel theses for generalized Hankel operators}}, url = {{http://dx.doi.org/10.1007/s00028-013-0209-z}}, doi = {{10.1007/s00028-013-0209-z}}, volume = {{14}}, year = {{2014}}, }