A note on the Hall–Mergelyan theme
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 1, pp. 164-168
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Let $\mu$ be a measure supported by the points $e^k$, $k=1,2,\dots,$ with the weights $\mu_k=e^{sk^2/2}$ where $s>1$ is a parameter. Then the polynomials are dense in the space$\mathcal L^p(\mu)$ for $p and are not dense in the space $\mathcal L^p(\mu)$ for $p. This answers the question posed by Christian Berg and Jens Peter Reus Christensen.
@article{JMAG_1996_3_1_a14,
author = {M. L. Sodin},
title = {A note on the {Hall{\textendash}Mergelyan} theme},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {164--168},
year = {1996},
volume = {3},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a14/}
}
M. L. Sodin. A note on the Hall–Mergelyan theme. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 1, pp. 164-168. http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a14/