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On cosine families

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Abstract

We prove that, in a sequentially complete locally convex Hausdorff space X, every locally equicontinuous strongly continuous cosine family is uniquely determined by its infinitesimal generator. If, in addition, X is a barrelled space, we give a generalization of uniqueness theorem for strongly continuous cosine families. Equipped with these results, we present a necessary and sufficient condition for a linear continuous operator to be the infinitesimal generator of a strongly continuous cosine family.

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Authors and Affiliations

  1. Faculty of Sciences Dhar-Mehraz, Department of Mathematics, Sidi Mohamed Ben Abdellah University, B.P. 1796, Fès-Atlas, 30003, Morocco

    Rachid Ameziane Hassani, Abdelkhalek El Amrani & Khalil Moussa Ouja

  2. École Normale Supérieure, Department of Mathematics, Sidi Mohamed Ben Abdellah University, B.P 5206, Bensouda-Fès, Morocco

    Aziz Blali

Authors
  1. Rachid Ameziane Hassani
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  2. Aziz Blali
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  3. Abdelkhalek El Amrani
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  4. Khalil Moussa Ouja
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Correspondence to Khalil Moussa Ouja.

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Ameziane Hassani, R., Blali, A., El Amrani, A. et al. On cosine families. Rend. Circ. Mat. Palermo, II. Ser 71, 725–735 (2022). https://doi.org/10.1007/s12215-021-00635-5

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  • DOI: https://doi.org/10.1007/s12215-021-00635-5

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