Geodesic
Complete and incomplete systems of exponentials in spaces with a power weight on a half-line
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2014), pp. 52-55

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We essentially widen the class of sequences $\lambda_n$ for which the completeness (non-completeness) of system of exponentials $e^{-\lambda_nt},~{\rm Re}\lambda_n>0$ is proved in the spaces $L^p(\mathbb{R}_+,t^\alpha dt),~\alpha>-1$. The proof uses the invariance of completeness relative to the change of the weight $t^\alpha$ by the weight $(1+t)^\alpha$; this fact is also proved here. 
@article{VMUMM_2014_2_a7,
     author = {A. M. Sedletskii},
     title = {Complete and incomplete systems of exponentials in spaces with a power weight on a half-line},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {52--55},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_2_a7/}
}
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A. M. Sedletskii. Complete and incomplete systems of exponentials in spaces with a power weight on a half-line. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2014), pp. 52-55. http://geodesic.mathdoc.fr/item/VMUMM_2014_2_a7/