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In this paper, we study the sampling theory for non-decaying signals in mixed Lebesgue spaces. First, we give some Riesz-type bounds, which connect the weighted discrete norms of the samples to the weighted continuous norms of original and interpolated signals. Then, we prove that the sampling and reconstruction through the Riesz-type bounds are stable when the generated kernel is in the appropriate mixed Wiener amalgam spaces.

A sampling theory for non-decaying signals in mixed Lebesgue spaces