Abstract
We study the structural and linear topological properties of the space \(\dot{\mathcal {B}}^{\prime *}_{\omega }\) of ultradistributions vanishing at infinity (with respect to a weight function \(\omega \)). Particularly, we show the first structure theorem for \(\dot{\mathcal {B}}^{\prime *}_{\omega }\) under weaker hypotheses than were known so far. As an application, we determine the structure of the S-asymptotic behavior of ultradistributions.
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Acknowledgements
A. Debrouwere was supported by FWO-Vlaanderen via the postdoctoral Grant 12T0519N. L. Neyt gratefully acknowledges support by Ghent University through the BOF-Grant 01J11615. The work of J. Vindas was supported by Ghent University through the BOF-Grants 01J11615 and 01J04017.
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Communicated by Jose Bonet.
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Debrouwere, A., Neyt, L. & Vindas, J. On the space of ultradistributions vanishing at infinity. Banach J. Math. Anal. 14, 915–934 (2020). https://doi.org/10.1007/s43037-019-00045-x
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DOI: https://doi.org/10.1007/s43037-019-00045-x
Keywords
- The space of ultradistributions vanishing at infinity
- The first structure theorem
- S-asymptotics
- The short-time Fourier transform