Abstract: We prove Landis-type results for both the semidiscrete heat and the stationary discrete Schrödinger equations. For the semidiscrete heat equation we show that, under the assumption of two-time spatial decay conditions on the solution u, then necessarily u ? 0. For the stationary discrete Schrödinger equation we deduce that, under a vanishing condition at infinity on the solution u, then u ? 0. In order to obtain such results, we demonstrate suitable quantitative upper and lower estimates for the L2-norm of the solution within a spatial lattice (hZ)d. These estimates manifest an interpolation phenomenon between continuum and discrete.

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