Abstract
The unitarity conditions (UC) for the resonance-particle amplitude are explicitly deduced from the exact three-body UC. In case where two pairs out of three particles resonate an additional term changes the quasi two-body form of the UC. Its presence is shown to guarantee the real analyticity of the resonance-particle amplitude. The UC obtained possess two classes of solutions, singular or regular at the Peierls points. Comparison with the Fredholm denominator of the Faddeev equation for the resonance-particle amplitude enables one to choose the unique solution having no Peierls singularities. The linear integral equation for the denominator of the resonance-particle amplitude is explicitly written and discussed.
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