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

 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 $n>n_0(p,\lambda)$.

Full text: PDF file (493 kB)

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

Bibliographic databases:

UDC: 517.5

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}