On representation of functions as convolution transforms

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Necessary and sufficient conditions on f(x) to be a convolution-Stieltjes transform of α(t) where α(t) is such that the transform converges absolutely, are given. The above result is given for Convolution transforms with variation diminishing kernels of class I.


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Entrata in Redazione il 19 aprile 1971.

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Ditzian, Z. On representation of functions as convolution transforms. Annali di Matematica 92, 95–106 (1972).

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