General $n$-dimensional Tauberian problems with application to the Laplace- and Stieltjes transforms

Lennart Frennemo

Abstract


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.

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DOI: http://dx.doi.org/10.7146/math.scand.a-14390

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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