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Zapiski Nauchnykh Seminarov 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
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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.
Received: 10.08.2009
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 165, Issue 4, Pages 431–434
DOI: https://doi.org/10.1007/s10958-010-9810-7
Bibliographic databases:
UDC: 517.5
Language: Russian
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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949287973}
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