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Mat. Zametki, 1978, Volume 23, Issue 2, Pages 223–230 (Mi mz8135)  

Algebraic polynomial bases of space $L_p$

Z. A. Chanturiya

Tbilisi State University

Abstract: Let $\{\varphi_n\}$ be a system, close to the orthonormal complete system $\{\chi_n\}$. An estimate is obtained for the deviation of the system $\{f_n\}$, obtained from $\{\varphi_n\}$ by Schmidt's method, from the system $\{\chi_n\}$. This estimate is used to show that, in any $L_p(-1,1)$, with $p\in(1,4/3]\cup[4,\infty)$, and for any $\lambda>\pi e/4=2,13…$, there exists an orthogonal algebraic system $\{P_n(x)\}_{n=0}^\infty$, forming a basis in $L_p$ and such that $\nu_n=\deg P_n(x)\le\lambda n$ for $n>n_0(p,\lambda)$.

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English version:
Mathematical Notes, 1978, 23:2, 123–127

Bibliographic databases:

UDC: 517.5
Received: 29.05.1976

Citation: Z. A. Chanturiya, “Algebraic polynomial bases of space $L_p$”, Mat. Zametki, 23:2 (1978), 223–230; Math. Notes, 23:2 (1978), 123–127

Citation in format AMSBIB
\Bibitem{Cha78}
\by Z.~A.~Chanturiya
\paper Algebraic polynomial bases of space $L_p$
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 2
\pages 223--230
\mathnet{http://mi.mathnet.ru/mz8135}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=492665}
\zmath{https://zbmath.org/?q=an:0404.42015|0381.42007}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 2
\pages 123--127
\crossref{https://doi.org/10.1007/BF01153151}


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