Geodesic
Divergent Fourier series with respect to orthonormalized systems of smooth functions
Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 69-78.

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In this paper it is proved that for any function $f\in L^2[-\pi;\pi]$, $\|f\|_2>0$, there exists a complete orthonormalized system of uniformly bounded trigonometric polynomials with respect to which the Fourier series of this function is divergent almost everywhere in the interval $[-\pi;\pi]$. 
@article{MZM_1976_20_1_a7,
     author = {N. T. Anisimova},
     title = {Divergent {Fourier} series with respect to orthonormalized systems of smooth functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {69--78},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a7/}
}
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N. T. Anisimova. Divergent Fourier series with respect to orthonormalized systems of smooth functions. Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 69-78. http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a7/