Abstract:
It is shown that the main uniqueness properties of a multiple trigonometric series are equivalent to similar properties of the corresponding series with respect to a multiple Haar system with variable coefficients. Uniqueness theorems for multiple trigonometric series are proved under different conditions on the coefficients and on the derivative with respect to random binary nets of the sums of the series resulting from their single integration.
Keywords:differentiation with respect to random binary nets, multiple trigonometric series, multiple Haar system, Fourier series, Lebesgue measure.
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