Geodesic
Coefficients of convergent multiple Haar series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 67-71

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It is well-known that if a multiple trigonometric series almost everywhere converges in the square or restricted rectangular sense to a finite function, then its coefficients grow slower than any exponential function. In this paper we prove the existence of a multiple Haar series that converges in the square or restricted rectangular sense to a finite function and contains a subsequence of coefficients that grows faster than any sequence defined an advance. Moreover, we show that for such series conditions of the Arutyunyan–Talalyan type can be violated at some points.
Keywords: Haar system, multiple Haar series, convergence in the square sense, convergence in the restricted rectangular sense
Mots-clés : Cantor–Lebesgue type theorems. 
@article{IVM_2012_1_a8,
     author = {M. G. Plotnikov},
     title = {Coefficients of convergent multiple {Haar} series},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--71},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_1_a8/}
}
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M. G. Plotnikov. Coefficients of convergent multiple Haar series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 67-71. http://geodesic.mathdoc.fr/item/IVM_2012_1_a8/