Subordination for sequentially equicontinuous equibounded $$C_0$$-semigroups

Kruse, Karsten; Meichsner, Jan; Seifert, Christian

doi:10.1007/s00028-021-00700-7

Cited by 9 publications

(2 citation statements)

References 39 publications

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“…Let P γ be a directed system of seminorms that generates the mixed topology γ. Due to [35,Lemma 5.5 (a), p. 2680] and [36, Remark 2.3 (c), p. 3] we may choose P γ such that x = sup pγ∈Pγ p γ (x) for all x ∈ X. We start with noting that the map s → T (s)AR(λ, A)h is γ-Pettis integrable on [0, t] and…”

Section: K Kruse and F L Schwenningermentioning

confidence: 99%

Sun Dual Theory For Bi-Continuous Semigroups

Kruse,

Schwenninger

2024

Anal Math

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The sun dual space corresponding to a strongly continuous semigroup is a known concept when dealing with dual semigroups, which are in general only weak $$^*$$ ∗ -continuous. In this paper we develop a corresponding theory for bi-continuous semigroups under mild assumptions on the involved locally convex topologies. We also discuss sun reflexivity and Favard spaces in this context, extending classical results by van Neerven.

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Section: K Kruse and F L Schwenningermentioning

confidence: 99%

Sun Dual Theory For Bi-Continuous Semigroups

Kruse,

Schwenninger

2024

Anal Math

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“…We will only deal with strongly continuous semigroups in the presentation; however, note that subordination can also be performed in more general settings (see e.g. [KMS21]), in particular for dual semigroups of strongly continuous semigroups.…”

Section: Final State Observability For Subordinated Semigroupsmentioning

confidence: 99%

Final State Observability in Banach spaces with applications to Subordination and Semigroups induced by L{é}vy processes

Gallaun¹,

Meichsner²,

Seifert³

2022

Preprint

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This paper generalizes the abstract method of proving an observability estimate by combining an uncertainty principle and a dissipation estimate. In these estimates we allow for a large class of growth/decay rates satisfying an integrability condition. In contrast to previous results, we use an iterative argument which enables us to give an asymptotically sharp estimate for the observation constant and which is explicit in the model parameters. We give two types of applications where the extension of the growth/decay rates naturally appear. By exploiting subordination techniques we show how the dissipation estimate of a semigroup transfers to subordinated semigroups. Furthermore, we apply our results to semigroups related to Lévy processes.

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Sufficient Criteria for Stabilization Properties in Banach Spaces

Egidi,

Gallaun,

Seifert

et al. 2024

Integr. Equ. Oper. Theory

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We study abstract sufficient criteria for cost-uniform open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a sufficient condition for null-controllability in Banach spaces given by an uncertainty principle and a dissipation estimate. For stabilizability these estimates are only needed for a single spectral parameter and, in particular, their constants do not depend on the growth rate w.r.t. this parameter. Our result unifies and generalizes earlier results obtained in the context of Hilbert spaces. As an application we consider fractional powers of elliptic differential operators with constant coefficients in $$L_p(\mathbb {R}^d)$$ L p ( R d ) for $$p\in [1,\infty )$$ p ∈ [ 1 , ∞ ) and thick control sets.

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Subordination for sequentially equicontinuous equibounded $$C_0$$-semigroups

Abstract: We consider operators A on a sequentially complete Hausdorff locally convex space X such that $$-A$$ - A generates a (sequentially) equicontinuous equibounded $$C_0$$ C 0 -semigroup. For every Bernstein function f we show that $$-f(A)$$ - f ( A … Show more

Cited by 9 publications

References 39 publications

Sun Dual Theory For Bi-Continuous Semigroups

Sun Dual Theory For Bi-Continuous Semigroups

Final State Observability in Banach spaces with applications to Subordination and Semigroups induced by L{é}vy processes

Sufficient Criteria for Stabilization Properties in Banach Spaces

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