Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. Hardy uncertainty principle, convexity and parabolic evolutions. (English) Zbl 1356.35045 Commun. Math. Phys. 346, No. 2, 667-678 (2016). Summary: We give a new proof of the \(L^{2}\) version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay bounds for solutions to the heat equation with Gaussian decay at a future time. We extend the result to heat equations with lower order variable coefficient. Cited in 10 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 42B05 Fourier series and coefficients in several variables 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35K15 Initial value problems for second-order parabolic equations 35Q41 Time-dependent Schrödinger equations and Dirac equations Keywords:log-convexity properties; optimal Gaussian decay bounds; lower order variable coefficient PDFBibTeX XMLCite \textit{L. Escauriaza} et al., Commun. Math. Phys. 346, No. 2, 667--678 (2016; Zbl 1356.35045) Full Text: DOI arXiv Link References: [1] Bonami, A., Demange, B.: A survey on uncertainty principles related to quadratic forms. In: Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations. Collect. Math. 1-36 (2006) · Zbl 1107.30021 [2] Bonami A., Demange B., Jaming P.: Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms. Rev. Mat. 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