The asymptotic properties of the Fourier-Stiltjes transform of a class of generalized Bernoulli convolutions are investigated.
The emphasis is on finding necessary and sufficient conditions for the equality of zero, unity of the upper bound $L$ at infinity of the modulus of the corresponding Fourier-Stiltjes transform. The value of the quantity $L$ is calculated under certain conditions imposed on the elements of the corresponding convolution.

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