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Inverse closedness and localization in extended Gevrey regularity

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Abstract

We consider classes \( \mathcal {E}_{\tau ,\sigma }(U)\) of ultradifferentiable functions which are extension of Gevrey classes, and prove that such classes are inverse closed. This result is used to construct an element from \( \mathcal {E}_{\tau ,\sigma }(U)\) which is not a Gevrey regular function. Furthermore, we show that the singular support of a distribution \(u\in \mathcal {D}'(U)\) related to local regularity in \( \mathcal {E}_{\tau ,\sigma }(U)\) coincides with the standard projection of the corresponding wave front set \( {\text {WF}}_{\tau ,\sigma }(u)\).

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Acknowledgements

This research is supported by Ministry of Education, Science and Technological Development of Serbia through the Project no. 174024.

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Authors and Affiliations

  1. Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia

    Nenad Teofanov

  2. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    Filip Tomić

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  1. Nenad Teofanov
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  2. Filip Tomić
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Correspondence to Nenad Teofanov.

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Dedicated to the memory of Todor Gramchev.

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Teofanov, N., Tomić, F. Inverse closedness and localization in extended Gevrey regularity. J. Pseudo-Differ. Oper. Appl. 8, 411–421 (2017). https://doi.org/10.1007/s11868-017-0205-0

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  • DOI: https://doi.org/10.1007/s11868-017-0205-0

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