Geodesic
Divergent Fourier series of integrable functions with respect to orthonormal systems
Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 717-724.

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There exist two orthonormal systems such that the Fourier series of each function $f\in L[0,1]$, $f\ne0$, with respect to at least one of these systems diverges on a set of positive measure. 
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A. S. Krantsberg. Divergent Fourier series of integrable functions with respect to orthonormal systems. Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 717-724. http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a9/

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