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Generalized Evolution Semigroups and General Dichotomies

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Abstract

We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding generators, our results directly apply to a wide class of dichotomies, such as those with time-varying rate of change.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei 2, 300006, Timişoara, Romania

    Nicolae Lupa

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Oradea, Universităţii St. 1, 410087, Oradea, Romania

    Liviu Horia Popescu

Authors
  1. Nicolae Lupa
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  2. Liviu Horia Popescu
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All authors contributed to the study conception and design, commented on previous versions of the manuscript, read and approved the final manuscript.

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Correspondence to Nicolae Lupa.

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Lupa, N., Popescu, L.H. Generalized Evolution Semigroups and General Dichotomies. Results Math 78, 112 (2023). https://doi.org/10.1007/s00025-023-01896-5

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