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Admissibility of Control and Observation Operators for Semigroups: A Survey

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Current Trends in Operator Theory and its Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 149))

Abstract

This paper reviews the literature on admissibility of control and observation operators for semigroups, presenting many recent results in this approach to infinite-dimensional systems theory. The themes discussed include duality between control and observation, conditions for admissibility expressed in terms of the resolvent of the infinitesimal generator, results for normal semigroups and their links with Carleson measures, properties of shift semigroups and Hankel operators, contraction semigroups and functional models, Hille-Yosida conditions on the resolvent, and weak admissibility.

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Authors and Affiliations

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

    Birgit Jacob

  2. University of Leeds, School of Mathematics, Leeds, LS2 9JT, UK

    Jonathan R. Partington

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  1. Birgit Jacob
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Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball  & Martin Klaus  & 

  2. Department of Mathematics, University of California, La Jolla, CA, 92093, USA

    J. William Helton

  3. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Leiba Rodman

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Jacob, B., Partington, J.R. (2004). Admissibility of Control and Observation Operators for Semigroups: A Survey. In: Ball, J.A., Helton, J.W., Klaus, M., Rodman, L. (eds) Current Trends in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 149. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7881-4_10

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