Abstract
For a locally compact group, the property of rapid decay (property (RD)) gives a control on the convolutor norm of any compactly supported function in terms of its \(L^2\)-norm and the diameter of its support. We investigate in this paper the algebraic structure of compactly generated p-adic groups that have property (RD). We prove in particular that an algebraic group over \(\mathbb Q_p\) which is compactly generated as well as its radical has property (RD) if and only if it is reductive.
Dedicated to the memory of Professor Takaaki Nomura.
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Acknowledgements
The author would like to express his gratitude to A. Baklouti and H. Ishi, the organizers of the 6th Tunisian-Japanese Conference of “Geometric and Harmonic Analysis on homogeneous spaces and Applications” in honor of Professor Takaaki Nomura, for their warm hospitality during the stimulating conference held in Djerba Island. He would like to thank warmly Professor Baklouti for the interest he has shown in the rapid decay property and for fruitful discussions.
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Mustapha, S. (2021). Rapid Decay Property for Algebraic p-Adic Groups. In: Baklouti, A., Ishi, H. (eds) Geometric and Harmonic Analysis on Homogeneous Spaces and Applications . TJC 2019. Springer Proceedings in Mathematics & Statistics, vol 366. Springer, Cham. https://doi.org/10.1007/978-3-030-78346-4_11
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DOI: https://doi.org/10.1007/978-3-030-78346-4_11
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