We study holomorphic solutions for convolution equations in tube domains. Let \mathcal{O}
τ be the sheaf of holomorphic functions in tube domains on the purely imaginary space √{-1}\bm{R}
n and \mathscr{S} the complex 0→ \mathcal{O}
τ→^{μ
*}\mathcal{O}
τ→ 0 generated by the convolution operator μ
* with hyperfunction kernel μ. In this paper, we give a new definition of“the characteristic set”Char(μ
*) using terms of zeros of the total symbol of μ
*, and show, uNδer the abstract coNδition (S), the equivalence between two notions of characteristics outside of the zero section T_{√{-1}\bm{R}
n}
*(√{-1}\bm{R}
n). Moreover we conclude that the micro-support SS(\mathscr{S}) of \mathscr{S} coincides with the characteristics Char(μ
*).
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