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Differentiation with respect to random binary nets and uniqueness of multiple trigonometric series

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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.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, Armenia

    A. A. Talalyan

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  1. A. A. Talalyan
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Correspondence to A. A. Talalyan.

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Original Russian Text © A. A. Talalyan, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 1, pp. 78–96.

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Talalyan, A.A. Differentiation with respect to random binary nets and uniqueness of multiple trigonometric series. Math Notes 88, 79–96 (2010). https://doi.org/10.1134/S0001434610070084

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  • DOI: https://doi.org/10.1134/S0001434610070084

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