Density questions in the classical theory of moments
Annales de l'Institut Fourier, Volume 31 (1981) no. 3, p. 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 1p2, 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 1p2, 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.

@article{AIF_1981__31_3_99_0,
     author = {Berg, Christian and Christensen, J. P. Reus},
     title = {Density questions in the classical theory of moments},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {31},
     number = {3},
     year = {1981},
     pages = {99-114},
     doi = {10.5802/aif.840},
     zbl = {0437.42007},
     mrnumber = {84i:44006},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1981__31_3_99_0}
}
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. http://www.numdam.org/item/AIF_1981__31_3_99_0/

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