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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

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}