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Mat. Sb. (N.S.), 1971, Volume 84(126), Number 3, Pages 406–424 (Mi msb3081)  

On completeness of a system of functions that are close to power functions

L. A. Leont'eva


Abstract: We obtain necessary and sufficient conditions for the completeness of the system $\{f_n(x)=x^{\lambda_n}[1+\varepsilon_n(x)]\}$ in $L_p[0, a]$, where $\varepsilon_n(x)\in L_p[0, a]$, $\varlimsup_{n\to\infty}\frac{\ln m_n}{\lambda_n}<0$, $m_n = \|\varepsilon_n(x)\|_{L_p[0, a]}$, $n=1,2,…$; $1<p<\infty$.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 13:3, 400–418

Bibliographic databases:

UDC: 517.51
MSC: Primary 42A64; Secondary 30A18, 30A66
Received: 07.01.1970

Citation: L. A. Leont'eva, “On completeness of a system of functions that are close to power functions”, Mat. Sb. (N.S.), 84(126):3 (1971), 406–424; Math. USSR-Sb., 13:3 (1971), 400–418

Citation in format AMSBIB
\Bibitem{Leo71}
\by L.~A.~Leont'eva
\paper On completeness of a~system of functions that are close to power functions
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 84(126)
\issue 3
\pages 406--424
\mathnet{http://mi.mathnet.ru/msb3081}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=280917}
\zmath{https://zbmath.org/?q=an:0209.09703|0239.42025}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 13
\issue 3
\pages 400--418
\crossref{https://doi.org/10.1070/SM1971v013n03ABEH003690}


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