On the characteristics for convolution equations in tube domains

抄録

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^*).