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Topologies in the Set of Rapidly Decreasing Distributions

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Semigroups of Operators – Theory and Applications (SOTA 2018)

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Abstract

Two topologies are introduced in the set of rapidly decreasing distributions on Euclidean space. One of these turns the standard convergence structure carried by this set into a topological convergence structure. The other allows the set in question to be topologically identified with the multiplier space for the Schwartz space of rapidly decreasing functions.

To the memory of Professor Janusz Mika

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Acknowledgements

The author expresses his warmest thanks to the Referee whose remarks and suggestions resulted in fundamental amelioration of the paper. The author is very grateful to Professors Adam Bobrowski and Wojciech Chojnacki for their kind help in correcting the paper and offering valuable linguistic hints.

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Authors and Affiliations

  1. ul. Tymiankowa 56 m. 4, 20-542, Lublin, Poland

    Jan Kisyński

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  1. Jan Kisyński
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Correspondence to Jan Kisyński .

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Editors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield, South Africa

    Jacek Banasiak

  2. Department of Mathematics, Lublin University of Technology, Lublin, Poland

    Adam Bobrowski

  3. Institute of Applied Mathematics and Mechanics, University of Warsaw, Warsaw, Poland

    Mirosław Lachowicz

  4. Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland

    Yuri Tomilov

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Kisyński, J. (2020). Topologies in the Set of Rapidly Decreasing Distributions. In: Banasiak, J., Bobrowski, A., Lachowicz, M., Tomilov, Y. (eds) Semigroups of Operators – Theory and Applications. SOTA 2018. Springer Proceedings in Mathematics & Statistics, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-030-46079-2_1

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