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The Haar orthogonal system had been constructed in 1909 [7] as an answer on the question by D. Hilbert: is there exist an orthogonal system on the segment [0,1] such that the Fourier series of any continuous function with respect to this system converges uniformly on [0,1] to this function? The Haar system has many applications in the theory of orthogonal series and applied mathematics (see [9], [11]...