Analogues of Miyachi, cowling-price and Morgan theorems for compact extensions of ℝ n

Salma Azaouzi (), Ali Baklouti () and Mounir Elloumi ()
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Salma Azaouzi: Sfax University
Ali Baklouti: Sfax University
Mounir Elloumi: Sfax University

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 5, 587-604

Abstract: Abstract Let K be a compact subgroup of automorphisms of ℝ n . We formulate and prove an analogue of Miyachi’s theorem for the semi-direct product K ⋉ ℝ n . This allows us to solve the sharpness problems in the theorem of Cowling-Price and in the L p − L q analogue of Morgan theorem for any compact extension of ℝ n . These upshots are proved using the representations theory and the Plancherel formula for the group Fourier transform.

Keywords: Uncertainty principle; Fourier transform; Plancherel formula (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0031-x

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