no. 3
Density questions in the classical theory of moments
Annales de l'Institut Fourier, Volume 31 (1981) no. 3, pp. 99-114.

Let μ be a positive Radon measure on the real line having moments of all orders. We prove that the set P of polynomials is note dense in L p (R,μ) for any p>2, if μ is indeterminate. If μ is determinate, then P is dense in L p (R,μ) for 1≤p≤2, but not necessarily for p>2. The compact convex set of positive Radon measures with same moments as μ is studied in some details.

Soit μ une mesure de Radon positive sur la droite dont tous les moments existent. Nous démontrons que l’ensemble P des polynômes n’est pas dense dans L p (R,μ) pour p>2, si μ est indéterminée. Si μ est déterminée P est dense dans L p (R,μ) pour 1≤p≤2, mais non nécessairement pour p>2. Ensuite, nous étudions l’ensemble convexe et compact des mesures de Radon positives admettant les mêmes moments que μ.

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     title = {Density questions in the classical theory of moments},
     journal = {Annales de l'Institut Fourier},
     pages = {99--114},
     publisher = {Institut Fourier},
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     volume = {31},
     number = {3},
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Berg, Christian; Christensen, J. P. Reus. Density questions in the classical theory of moments. Annales de l'Institut Fourier, Volume 31 (1981) no. 3, pp. 99-114. doi : 10.5802/aif.840. https://aif.centre-mersenne.org/articles/10.5802/aif.840/

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