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Admissible control and observation operators for Volterra integral equations

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Journal of Evolution Equations Aims and scope Submit manuscript

Abstract.

The admissibility of observation operators and control operators for linear Volterra systems is studied by means of the theory of composition operators on Hardy spaces.Under certain assumptions it is shown to be equivalent to admissibility for the classical Cauchy problem. A duality between control and observation operators is also established,extending known results for the Cauchy problem,which is a special case.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Dortmund, 44221, Dortmund, Germany

    Birgit Jacob

  2. School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom

    Jonathan R. Partington

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  1. Birgit Jacob
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  2. Jonathan R. Partington
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Correspondence to Birgit Jacob.

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Jacob, B., Partington, J.R. Admissible control and observation operators for Volterra integral equations. J.evol.equ. 4, 333–343 (2004). https://doi.org/10.1007/s00028-004-0152-0

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  • DOI: https://doi.org/10.1007/s00028-004-0152-0

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