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Mat. Zametki, 1977, Volume 22, Issue 5, Pages 711–728 (Mi mz8094)  

Order of growth of the degrees of a polynomial basis of a space of continuous functions

V. N. Temlyakov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: The problem under consideration is the one posed independently by C. Foias and I. Singer and by P. L. Ul'yanov concerning the minimal growth of the degrees $\nu_n$ of a polynomial basis $\{t_n(x)\}_0^\infty$ of a space of continuous functions. It is shown that there exist an absolute constant $C$ and a polynomial basis $\{t_n(x)\}_0^\infty$ such that
$$ \nu_n\le C(n\ln^+\ln(n+1)+1),\quad n=0,1,2,…$$
The feasibility of the method employed is also considered.

Full text: PDF file (1034 kB)

English version:
Mathematical Notes, 1977, 22:5, 888–898

Bibliographic databases:

UDC: 517.5
Received: 28.01.1977

Citation: V. N. Temlyakov, “Order of growth of the degrees of a polynomial basis of a space of continuous functions”, Mat. Zametki, 22:5 (1977), 711–728; Math. Notes, 22:5 (1977), 888–898

Citation in format AMSBIB
\Bibitem{Tem77}
\by V.~N.~Temlyakov
\paper Order of growth of the degrees of a~polynomial basis of a~space of continuous functions
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 5
\pages 711--728
\mathnet{http://mi.mathnet.ru/mz8094}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=493295}
\zmath{https://zbmath.org/?q=an:0373.46025}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 888--898
\crossref{https://doi.org/10.1007/BF01098354}


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