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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 12, Issue 1, Pages 29–36 (Mi mz9843)

A property of a system of functions close to exponential functions

L. A. Leont'eva

Moscow Physicotechnical Institute

Abstract: We consider the system $\{f_n(x)=x^{\lambda_n}[1+\varepsilon_n(x)]\}$ in the interval $[a,b]$ ($0\leqslant a<b<\infty$). Under certain conditions on $\lambda_n>0$ and $\varepsilon_n(x)$ such as the condition $\varlimsup\limits_{n\to\infty}\frac{\ln m_n}{\lambda_n}>0$, $m_n=||\varepsilon_n(x)||_{L_p[a,b]}$, we obtain a bound for the coefficients of the polynomial $P(x)=\sum c_nf_n(x)$ in terms of $||P(x)||_{L_p[a,b]}$. It is found that this bound is not valid without this condition (assuming the other conditions to remain the same).

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English version:
Mathematical Notes, 1972, 12:1, 450–454

Bibliographic databases:

UDC: 517.5

Citation: L. A. Leont'eva, “A property of a system of functions close to exponential functions”, Mat. Zametki, 12:1 (1972), 29–36; Math. Notes, 12:1 (1972), 450–454

Citation in format AMSBIB
\Bibitem{Leo72} \by L.~A.~Leont'eva \paper A property of a system of functions close to exponential functions \jour Mat. Zametki \yr 1972 \vol 12 \issue 1 \pages 29--36 \mathnet{http://mi.mathnet.ru/mz9843} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=318764} \zmath{https://zbmath.org/?q=an:0247.42010} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 1 \pages 450--454 \crossref{https://doi.org/10.1007/BF01094389}