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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
Received: 27.11.1970

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}


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