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Let ¡l be a bounded Borel measure and / be asymptotically almost periodic. Conditions are found which ensure that certain bounded solutions of the linear convolution integral equation g « fi = / are asymptotically almost periodic. This result is also extended to the case where the measure ¡i is replaced by a tempered distribution t for which convolution with bounded functions makes sense.doi:10.2307/2042320 fatcat:myvhihrulrhalfp5zzh23p5jfq