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 
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/
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     author = {A. M. Sedletskii},
     title = {Complete and incomplete systems of exponentials in spaces with a power weight on a half-line},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_2_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Sedletskii A.M., Klassy analiticheskikh preobrazovanii Fure i eksponentsialnye approksimatsii, Fizmatlit, M., 2005

[2] Sedletskii A.M., “Approksimatsiya tipa Myuntsa–Sasa v pryamykh proizvedeniyakh prostranstv”, Izv. RAN. Ser. matem., 70:5 (2006), 179–198 | DOI | MR | Zbl

[3] Sedletskii A.M., “Approksimatsiya tipa Myuntsa–Sasa v vesovykh prostranstvakh $L^p$ i nuli funktsii klassov Bergmana v poluploskosti”, Izv. vuzov. Matem., 2008, no. 5, 92–100 | MR | Zbl

[4] Khabibullin B.N., “Polnota sistem eksponent v prostranstvakh funktsii na luche i postoyannaya Korenblyuma–Seipa”, Ufim. matem. zhurn., 1:1 (2009), 77–83 | MR | Zbl