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| 2. |
- Jacob, B., et al.
(författare)
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The weighted Weiss conjecture and reproducing kernel theses for generalized Hankel operators
- 2014
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Ingår i: Journal of Evolution Equations. - : Springer Science and Business Media LLC. - 1424-3199 .- 1424-3202. ; 14:1, s. 85-120
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Tidskriftsartikel (refereegranskat)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.
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| 3. |
- Moberg, Christina, et al.
(författare)
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De unga gör helt rätt när de stämmer staten
- 2022
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Ingår i: Aftonbladet. - 1103-9000.
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- 1 620 forskare och lärare i forskarvärlden: Vi ställer oss bakom Auroras klimatkrav
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| 4. |
- Rydhe, Eskil
(författare)
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An Agler-type model theorem for C0-semigroups of Hilbert space contractions
- 2016
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 93:2, s. 420-438
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Tidskriftsartikel (refereegranskat)abstract
- We investigate suitable conditions for a C0-semigroup (T(t))t≥0 of Hilbert space contractions to be unitarily equivalent to the restriction of the adjoint shift semigroup (S∗γ(t))t≥0 to an invariant subspace of the standard weighted Bergman space Aγ−2(C+,K). It turns out that (T(t))t≥0 admits a model by (S∗γ(t))t≥0 if and only if its cogenerator is γ-hypercontractive and limt→0T(t)=0 in strong operator topology. We then discuss how such semigroups can be characterized without involving the cogenerator. A sufficient condition is that, for each t>0, the operator T(t) is γ-hypercontractive. Surprisingly, this condition is necessary if and only if γ is integer. The paper is concluded with a conjecture that would imply a more symmetric characterization.
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| 5. |
- Rydhe, Eskil
(författare)
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On laplace–carleson embeddings, and lp-mapping properties of the fourier transform
- 2020
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Ingår i: Arkiv för Matematik. - 0004-2080. ; 58:2, s. 437-457
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Tidskriftsartikel (refereegranskat)abstract
- We investigate so-called Laplace–Carleson embeddings for large exponents. In particular, we extend some results by Jacob, Partington, and Pott. We also discuss some related results for Sobolev-and Besov spaces, and mapping properties of the Fourier transform. These variants of the Hausdorff–Young theorem appear difficult to find in the literature. We conclude the paper with an example related to an open problem.
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| 6. |
- Rydhe, Eskil
(författare)
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On some topics in operator theory : An unfinished story about mathematical control
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis considers differentiation of non-negative, fractional order, composed with Hardy spacetypeHankel operators. H2-boundedness is characterized in terms of a reproducing kernel thesis.The setting of operator-valued symbols is considered, in which H2-boundedness is characterized interms of Carleson embeddings, provided that the order of differentiation is strictly positive. Somenew results are deduced for the zeroth order. The complexity of the Carleson embedding conditionsis demonstrated by means of examples. Natural corresponding factorization theorems are proved.Some results are phrased in terms of control theory. An attempt is made at describing Hilbert spacecontraction semigroups which can be modeled by a weighted backward shift.
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| 7. |
- Rydhe, Eskil
(författare)
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On the Characterization of Triebel–Lizorkin Type Spaces of Analytic Functions
- 2018
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Ingår i: Journal of Fourier Analysis and Applications. - : Springer Science and Business Media LLC. - 1069-5869 .- 1531-5851. ; 24:6, s. 1491-1517
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Tidskriftsartikel (refereegranskat)abstract
- We consider different characterizations of Triebel–Lizorkin type spaces of analytic functions on the unit disc. Even though our results appear in the folklore, detailed descriptions are hard to find, and in fact we are unable to discuss the full range of parameters. Without additional effort we work with vector-valued analytic functions, and also consider a generalized scale of function spaces, including for example so-called Q-spaces. The primary aim of this note is to generalize, and clarify, a remarkable result by Cohn and Verbitsky, on factorization of Triebel–Lizorkin spaces. Their result remains valid for functions taking values in an arbitrary Banach space, provided that the vector-valuedness “sits in the right factor”. On the other hand, if we impose vector-valuedness on the “wrong” factor, then the factorization theorem fails even for functions taking values in a separable Hilbert space.
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| 8. |
- Rydhe, Eskil
(författare)
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Two more counterexamples to the infinite dimensional carleson embedding theorem
- 2018
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Ingår i: International Mathematics Research Notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; 2018:24, s. 7655-7680
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Tidskriftsartikel (refereegranskat)abstract
- The existence of a counterexample to the infinite-dimensional Carleson embedding theorem has been established by Nazarov, Pisier, Treil, and Volberg. We provide an explicit construction of such an example. We also obtain a non-constructive example of particularly simple form; the density function of the measure (with respect to a certain weighted area measure) is the tensor-square of a Hilbert space-valued analytic function. This special structure of the measure has implications for Hankel-like operators appearing in control theory.
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| 9. |
- Rydhe, Eskil
(författare)
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Vectorial Hankel operators, Carleson embeddings, and notions of BMOA
- 2017
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Ingår i: Geometric and Functional Analysis. - : Springer Science and Business Media LLC. - 1016-443X .- 1420-8970. ; 27:2, s. 427-451
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Tidskriftsartikel (refereegranskat)abstract
- Let (Formula presented.) denote the space of (Formula presented.)-valued analytic functions (Formula presented.) for which the Hankel operator (Formula presented.) is (Formula presented.)-bounded. Obtaining concrete characterizations of (Formula presented.) has proven to be notoriously hard. Let (Formula presented.) denote fractional differentiation. Motivated originally by control theory, we characterize (Formula presented.)-boundedness of (Formula presented.), where (Formula presented.), in terms of a natural anti-analytic Carleson embedding condition. We obtain three notable corollaries: The first is that (Formula presented.) is not characterized by said embedding condition. The second is that when we add an adjoint embedding condition, we obtain a sufficient but not necessary condition for boundedness of (Formula presented.). The third is that there exists a bounded analytic function for which the associated anti-analytic Carleson embedding is unbounded. As a consequence, boundedness of an analytic Carleson embedding does not imply that the anti-analytic ditto is bounded. This answers a question by Nazarov, Pisier, Treil, and Volberg.
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| 10. |
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