A resolvent test for admissibility of Volterra observation operators

DOI10.1016/j.jmaa.2006.10.023zbMath1118.45008OpenAlexW2080416403WikidataQ56319279 ScholiaQ56319279MaRDI QIDQ882015

Birgit Jacob, Jonathan R. Partington

Publication date: 23 May 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.10.023

zbMATH Keywords

Hilbert spaceVolterra equationCauchy systemadmissibile control operatoradmissibile observation operator

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Operator-theoretic methods (93B28) Control/observation systems in abstract spaces (93C25) Systems of nonsingular linear integral equations (45F05)

Related Items (17)

Infinite-Time Admissibility of the Gurtin--Pipkin Systems in Hilbert Spaces ⋮ Characteristic of left invertible semigroups and admissibility of observation operators ⋮ A new approach to abstract linear viscoelastic equation in Hilbert space ⋮ On the regularity of solutions to the Moore-Gibson-Thompson equation: a perspective via wave equations with memory ⋮ Analysis and control of integro-differential Volterra equations with delays ⋮ Admissibility and Observability of Jeffreys Type of Overdamped Second Order Linear Systems ⋮ Uniform exponential stability of solutions to abstract Volterra equations ⋮ Asymptotic behavior and representation of solutions to a Volterra kind of equation with a singular kernel ⋮ Necessary conditions for the exact observability of systems on Hilbert spaces ⋮ On the complex inversion formula and admissibility for a class of Volterra systems ⋮ Strong stability and asymptotical almost periodicity of Volterra equations in Banach spaces ⋮ Skew-product semi-flows and non-autonomous control systems ⋮ Admissibility of the Observation Operators for Volterra systems with Exponential Kernels ⋮ Admissibility and controllability of diagonal Volterra equations with scalar inputs ⋮ Exponential stability of abstract Coleman-Gurtin equations in Hilbert spaces ⋮ Infinite-time exact observability of Volterra systems in Hilbert spaces ⋮ Infinite-Time Admissibility and Exact Observability of Volterra Systems

Cites Work

• Admissible control and observation operators for Volterra integral equations
• One-Parameter Semigroups for Linear Evolution Equations
• THE WEISS CONJECTURE FOR BOUNDED ANALYTIC SEMIGROUPS
• Admissibility of Control Operators for Solution Families to Volterra Integral Equations
• ADMISSIBLE AND WEAKLY ADMISSIBLE OBSERVATION OPERATORS FOR THE RIGHT SHIFT SEMIGROUP
• The Weiss conjecture on admissibility of observation operators for contraction semigroups
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