Abstract
We prove in this paper a generalization of Hardy’s theorem for Gabor transform in the setup of the semidirect product \(\mathbb {R}^n\rtimes K\), where K is a compact subgroup of automorphisms of \(\mathbb {R}^n\). We also solve the sharpness problem and thus obtain a complete analogue of Hardy’s theorem for Gabor transform. The representation theory and Plancherel formula are fundamental tools in the proof of our results.
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Communicated by Karlheinz Gröchenig.
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Smaoui, K. Hardy’s uncertainty principle for Gabor transform on compact extensions of \(\mathbb {R}^n\). Monatsh Math (2024). https://doi.org/10.1007/s00605-024-01960-4
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DOI: https://doi.org/10.1007/s00605-024-01960-4