Geodesic
An Approach to the Ultrametric Moment Problem
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 251-256 
W. H. Schikhof. An Approach to the Ultrametric Moment Problem. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 251-256. http://geodesic.mathdoc.fr/item/TM_2004_245_a24/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The classical Hausdorff–Widder–Bernstein theorem describes a 1–1 correspondence between probability measures $\mu$ on $[0,1]$ and a class of the so-called completely monotone functions $f$ on $(0,\infty)$ by means of the formula $f(x)=\int _0^1 s^x\,d\mu(s)$. In the present paper, we establish a non-Archimedean version of this theorem.

[1] De Grande-De Kimpe N., Khrennikov A., Van Hamme L., “The Fourier transform for $p$-adic tempered distributions”, $p$-Adic functional analysis, Lect. Notes Pure and Appl. Math., 207, M. Dekker, New York, 1999, 97–125 | MR

[2] Van Hamme L., “The $p$-adic moment problem”, $p$-Adic functional analysis, eds. N. De Grande-De Kimpe, S. Navarro, W. Schikhof, Univ. Santiago, Santiago, Chile, 1994, 151–163

[3] Martinez-Maurica J., Navarro S., “$p$-Adic Ascoli theorems”, Rev. Mat. Univ. Complut. Madrid, 3 (1990), 19–27 | MR | Zbl

[4] van Rooij A. C. M., Non-Archimedean functional analysis, M. Dekker, New York, 1978 | MR

[5] Schikhof W. H., Ultrametric calculus, Cambridge Stud. Adv. Math., 4, Cambridge Univ. Press, Cambridge, 1984 | MR | Zbl

[6] Schikhof W. H., “A perfect duality between $p$-adic Banach spaces and compactoids”, Indag. Math. N.S., 6 (1995), 325–339 | DOI | MR | Zbl