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Zap. Nauchn. Sem. POMI, 2009, Volume 366, Pages 5–12 (Mi znsl3478)  

Approximation in $L^p(\mathbb R^d)$, $0<p<1$, by linear combinations of the characteristic functions of balls

A. B. Aleksandrov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We prove that the translates of the characteristic function of a ball span $L^p(\mathbb R^d)$ provided $0<p<1$ and $d\ge2$. Similar approximation problems are considered for some other functions. Bibl. – 5 titles.

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English version:
Journal of Mathematical Sciences (New York), 2010, 165:4, 431–434

UDC: 517.5
Received: 10.08.2009

Citation: A. B. Aleksandrov, “Approximation in $L^p(\mathbb R^d)$, $0<p<1$, by linear combinations of the characteristic functions of balls”, Investigations on linear operators and function theory. Part 37, Zap. Nauchn. Sem. POMI, 366, POMI, St. Petersburg, 2009, 5–12; J. Math. Sci. (N. Y.), 165:4 (2010), 431–434

Citation in format AMSBIB
\Bibitem{Ale09}
\by A.~B.~Aleksandrov
\paper Approximation in $L^p(\mathbb R^d)$, $0<p<1$, by linear combinations of the characteristic functions of balls
\inbook Investigations on linear operators and function theory. Part~37
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 366
\pages 5--12
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3478}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 165
\issue 4
\pages 431--434
\crossref{https://doi.org/10.1007/s10958-010-9810-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949287973}


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