The Hardy Uncertainty Principle Revisited

2010/05/10 by M. Cowling, Michael Cowling, Cowling, M. +12 · 4 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.AP

paper · pdf · doi:10.48550/arxiv.1005.1543

arxiv created 2010/05/10 · openalex publication_date 2010/05/10 · arxiv updated 2010/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a real-variable proof of the Hardy uncertainty principle. The method is based on energy estimates for evolutions with positive viscosity, convexity properties of free waves with Gaussian decay at two different times, elliptic L²-estimates and the invertibility of the Fourier transform on L²(\Rn) and \mathcal S'(\Rn).

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• Dispersive equations with invariant measures
• Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement
• A theorem concerning Fourier transforms: A survey
• A dynamical Amrein-Berthier uncertainty principle

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