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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2014, Number 2, Pages 52–55
(Mi vmumm309)
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This article is cited in 2 scientific papers (total in 2 papers)
Short notes
Complete and incomplete systems of exponentials in spaces with a power weight on a half-line
A. M. Sedletskii Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
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.
Key words:
system of exponentials, completeness, weight space, convolution of functions.
Received: 07.02.2013
Citation:
A. M. Sedletskii, “Complete and incomplete systems of exponentials in spaces with a power weight on a half-line”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 2, 52–55; Moscow University Mathematics Bulletin, 69:2 (2014), 73–76
Linking options:
https://www.mathnet.ru/eng/vmumm309 https://www.mathnet.ru/eng/vmumm/y2014/i2/p52
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Abstract page: | 171 | Full-text PDF : | 48 | References: | 32 |
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