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.
G. V. Badalajan,The application of a convolution transform to the theory of generalized Stieltjes moment problem, Izv. Akad. Nauk SSSR Ser. Mat., Tom. 31 (1967). English translation: Math. USSR-Izvestija, Vol. I (1967), No. 3, pp. 475–514.
Z. Ditzian,Saturation class for inversion of convolution transform. To appear in the Proceeding of the Conference « On construction function theory », held in Budapest, Aug. 5 — Sept. 5.
I. I. Hirschman - D. V. Widder,The convolution transform, Princeton University Press, 1955.
D. Leviatan,A new approach to representation theory for convolution transforms, to appear in Pacific Journ. of Math.
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). https://doi.org/10.1007/BF02417939