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Operator Valued Fourier Multipliers and Stability of Strongly Continuous Semigroups

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Abstract.

Stability for strongly continuous semigroups on Banach spaces is described in terms of Lp–Fourier multiplier properties of the resolvent of the generator. A discrete version of this theory is developed, that lead to a description of the spectra of the semigroups in terms of discrete Lp–Fourier multipliers. Applications to stability of linear control systems on Banach spaces are given.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Yuri Latushkin

  2. Department of Mathematics, University of Tübingen, D-72076, Tübingen, Germany

    Frank Räbiger

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  1. Yuri Latushkin
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  2. Frank Räbiger
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Correspondence to Yuri Latushkin.

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Latushkin, Y., Räbiger, F. Operator Valued Fourier Multipliers and Stability of Strongly Continuous Semigroups. Integr. equ. oper. theory 51, 375–394 (2005). https://doi.org/10.1007/s00020-004-1349-x

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  • DOI: https://doi.org/10.1007/s00020-004-1349-x

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