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We consider multiscale functions of the type that are studied in averaging and homogenization theory and in multiscale modeling. Typical examples are two-scale functions f (x, x/ ), (0 < << 1) that are periodic in the second variable. We prove that under certain band limiting conditions these multiscale functions can be uniquely and stably recovered from non-uniform samples of optimal rate. The goal of this study is to establish the close relation between computational grids in multiscaledoi:10.1137/130936403 fatcat:4kox2ouajzfh3e7iehyknh4cle