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The weighted Weiss conjecture and reproducing kernel theses for generalized Hankel operators

Jacob, B.; Rydhe, Eskil LU and Wynn, A. (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)
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author
organization
publishing date
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
Birkhaüser
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
2014-04-30 12:14:50
date last changed
2017-04-09 03:01:47
@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},
  keyword      = {One parameter semigroups,admissibility,Hardy space,weighted Bergman,space,Hankel operators,reproducing kernel thesis},
  language     = {eng},
  number       = {1},
  pages        = {85--120},
  publisher    = {Birkhaüser},
  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},
  volume       = {14},
  year         = {2014},
}