Abstract
In this paper, we consider series of the Fourier coefficients of functions of several variables with respect to multiplicative systems generalizing the Walsh system. We present a sufficient condition for the convergence of these series in terms of the complete group modulus of continuity. We prove that this condition cannot be improved in the function classes H~ ~,'2 ..... ,~.. Let us present the relevant definitions and notation. Suppose that {p )}k~=t (J = 1, 2, ..., n) are
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