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Hardy uncertainty principle, convexity and parabolic evolutions. (English) Zbl 1356.35045

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.

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
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