Geodesic
On divergent Fourier series in orthogonal systems
Sbornik. Mathematics, Tome 22 (1974) no. 4, pp. 547-560

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In this work there is constructed a complete orthonormal system with respect to which the Fourier series of piecewise continuous non-identically-zero functions diverge a.e. There is also constructed an orthonormal system with respect to which the Fourier series of continuous functions converge a.e., while the Fourier series of bounded functions having at least one discontinuity of the first kind diverge a.e. Bibliography: 10 titles. 
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     author = {A. S. Krantsberg},
     title = {On divergent {Fourier} series in orthogonal systems},
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     url = {http://geodesic.mathdoc.fr/item/SM_1974_22_4_a4/}
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A. S. Krantsberg. On divergent Fourier series in orthogonal systems. Sbornik. Mathematics, Tome 22 (1974) no. 4, pp. 547-560. http://geodesic.mathdoc.fr/item/SM_1974_22_4_a4/