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Mat. Sb. (N.S.), 1986, Volume 130(172), Number 1(5), Pages 35–61 (Mi msb1849)  

On the recovery of the coefficients of a rearranged Haar series

G. M. Mushegyan


Abstract: The author has previously established that, for any rearrangement of a Haar series, if the rearranged series converges everywhere on $[0,1]$ to a bounded function $f(x)$ then the coefficients of the series can be recovered from the sum $f(x)$ using the formulas of Fourier; however, no analogous assertion holds, in general, for an arbitrary summable function $f$.
Generalizing his previous results, the author shows, in particular, that the theorem on the recovery of the coefficients of a rearranged Haar series goes over to functions of the class $L_2$, but not to the class $L_p$ for any $p<2$.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 58:1, 31–57

Bibliographic databases:

UDC: 517.51
MSC: 42C20, 42C10
Received: 01.08.1984 and 29.12.1985

Citation: G. M. Mushegyan, “On the recovery of the coefficients of a rearranged Haar series”, Mat. Sb. (N.S.), 130(172):1(5) (1986), 35–61; Math. USSR-Sb., 58:1 (1987), 31–57

Citation in format AMSBIB
\Bibitem{Mus86}
\by G.~M.~Mushegyan
\paper On the recovery of the coefficients of a rearranged Haar series
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 130(172)
\issue 1(5)
\pages 35--61
\mathnet{http://mi.mathnet.ru/msb1849}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=847342}
\zmath{https://zbmath.org/?q=an:0623.42013|0614.42015}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 1
\pages 31--57
\crossref{https://doi.org/10.1070/SM1987v058n01ABEH003091}


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