Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations Steve Huskey teachers and policy-makers across a

teachers and policy-makers across a range of fields

the dynamics of the family unit can start to shift

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Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations Steve Huskey teachers and policy-makers across aThis memoir is concerned with quantitative unique continuation estimates for equations involving a "sum of squares" operator L on a compact manifold M assuming: (i) the Chow Rashevski H? ormander condition ensuring the hypoellipticity of L,and(ii) the analyticity of M and the coefficients of L. The first result is the tunneling estimate ? L2(?) ? Ce? c? k 2 for normalized eigenfunctions ? of L from a nonempty open set ? ? M,wherek is the