Geodesic
On the coefficients of everywhere convergent series in some rearranged orthonormal systems
Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 107-132

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In this paper the author establishes the existence of a series $\sum a_{\nu_k}\cos\nu_kx+b_{\nu_k}\sin\nu_kx$ in some rearranged trigonometric system, which converges everywhere to a Lebesgue integrable function and whose coefficients $a_{\nu_k}$ and $b_{\nu_k}$, $k=1,2,\dots$, are not the Fourier–Lebesgue coefficients of this function. Similar results are established for the Haar system and some other systems. Bibliography: 17 titles. 
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     author = {G. M. Mushegyan},
     title = {On the coefficients of everywhere convergent series in some rearranged orthonormal systems},
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G. M. Mushegyan. On the coefficients of everywhere convergent series in some rearranged orthonormal systems. Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 107-132. http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a6/