Observability for Schrödinger and heat equations on lattices is equivalent to a local arithmetic condition on the set, revealing a discrete obstruction absent in Euclidean settings.
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ℓ¹→ℓ^∞ dispersive decay of order t^{-1/3} holds for the discrete Klein-Gordon equation on Z with small analytic quasi-periodic potentials, yielding Strichartz estimates and small-data global existence for the nonlinear problem.
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Observable sets for Schr\"odinger equations on combinatorial graphs
Observability for Schrödinger and heat equations on lattices is equivalent to a local arithmetic condition on the set, revealing a discrete obstruction absent in Euclidean settings.
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Dispersive estimates for discrete Klein-Gordon equations on one-dimensional lattice with quasi-periodic potentials
ℓ¹→ℓ^∞ dispersive decay of order t^{-1/3} holds for the discrete Klein-Gordon equation on Z with small analytic quasi-periodic potentials, yielding Strichartz estimates and small-data global existence for the nonlinear problem.