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In this paper the Corwin's conjecture is proved, which says that if d is a function analytic near ∞, then the hypoellipticity of the convolution operator Ad, defined by 
for every u ∊ S'(ℝn), implies that P(x)/ logx → ∞ as x → ∞, where P(x) is the distance from x ∊ ℝn to the set of complex zeros of d.
