Geodesic
Divergence of the Fourier series by generalized Haar systems at points of continuity of a~function
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2016), pp. 49-68

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We obtain a connection between the Dirichlet kernels and partial Fourier sums by generalized Haar and Walsh (Price) systems. Based on this, we establish an interrelation between convergence of the Fourier series by generalized Haar and Walsh (Price) systems. For any unbounded sequence we construct a model of continuous function on a group (and even on a segment $[0,1]$), whose Fourier series by generalized Haar system generated by this sequence, diverges at some point.
Keywords: Abelian group, modified segment $[0,1]$, continuity on modified segment $[0,1]$, systems of characters, Price's systems, generalized Haar's systems. 
@article{IVM_2016_1_a4,
     author = {V. I. Shcherbakov},
     title = {Divergence of the {Fourier} series by generalized {Haar} systems at points of continuity of a~function},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {49--68},
     publisher = {mathdoc},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_1_a4/}
}
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V. I. Shcherbakov. Divergence of the Fourier series by generalized Haar systems at points of continuity of a~function. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2016), pp. 49-68. http://geodesic.mathdoc.fr/item/IVM_2016_1_a4/