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A general theorem on the closure of translates in certain weighted spaces in $R^n$ is proved and as a consequence a general $n$-dimensional Tauberian theorem. This is applied to the $n$-dimensional Laplace transform and to the one-dimensional Stieltjes- and Weierstrass transforms.doi:10.7146/math.scand.a-14390 fatcat:l4sl4hbhyrfw7cbfti2zo22ddq