The M\"untz--Szasz problem
Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 91-103
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A condition is obtained on the placement of point $\lambda_n$ (in some sense, the final point) with which completeness of the system of functions $\{\exp(-\lambda_nx)\}$, $\operatorname{Re}\lambda_n>0$, in spaces $L^p$, $1\le p2$. is equivalent to divergence of the series $\sum\operatorname{Re}\lambda_n(1+|\lambda_n|^2)^{-1}$.
@article{MZM_1978_23_1_a9,
author = {V. I. Ladygin},
title = {The {M\"untz--Szasz} problem},
journal = {Matemati\v{c}eskie zametki},
pages = {91--103},
publisher = {mathdoc},
volume = {23},
number = {1},
year = {1978},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a9/}
}
V. I. Ladygin. The M\"untz--Szasz problem. Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 91-103. http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a9/