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On Limitations and Insufficiency of the Trotter-Kato Theorem

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Abstract

We exhibit examples of convergence of equibounded semigroups that cannot be captured by means of the classical Trotter-Kato theorem. This is done to substantiate the need for semigroup-theoretical tools that would supplement the Trotter-Kato theorem in dealing with convergence problems.

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  1. Institute of Mathematics of the Polish Academy of Sciences, Katowice branch on leave from Department of Mathematics, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, Poland

    Adam Bobrowski

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  1. Adam Bobrowski
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Correspondence to Adam Bobrowski.

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Bobrowski, A. On Limitations and Insufficiency of the Trotter-Kato Theorem. Semigroup Forum 75, 317–336 (2007). https://doi.org/10.1007/s00233-006-0676-4

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  • DOI: https://doi.org/10.1007/s00233-006-0676-4

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